Branches of Physics

Study of how things move without considering the cause of motion. This branch of physics only deals with describing how something is moving using quantities like distance, position, displacement, speed, velocity and acceleration.

Branches of Physics Study of how things move or don't move without considering the cause of motion. This branch of physics only deals with describing how something is moving using quantities like distance, position, displacement, speed, velocity and acceleration. Kinematics

Branches of Physics Study of why things move or don't move in a certain way. This branch of physics deals with a quantity called “net force”, which determines whether something accelerates or doesn't accelerate. This branch of physics deals with the causes of motion.

Branches of Physics Study of why things move or don't move in a certain way. This branch of physics deals with a quantity called “net force”, which determines whether something accelerates or doesn't accelerate. This branch of physics deals with the causes of motion. Dynamics

Branches of Physics Study of why things move or don't move in a certain way. This branch of physics deals with a quantity called “net force”, which determines whether something accelerates or doesn't accelerate. This branch of physics deals with the causes of motion. Dynamics Study of both how and why things move, or Kinematics + Dynamics = ??

Branches of Physics Study of why things move or don't move in a certain way. This branch of physics deals with a quantity called “net force”, which determines whether something accelerates or doesn't accelerate. This branch of physics deals with the causes of motion. Dynamics Study of both how and why things move, or Kinematics + Dynamics = Mechanics

Famous Kinematic Quantities

Tells us how far something travels along a path

Famous Kinematic Quantities Tells us how far something travels along a path = distance or change-in distance

Famous Kinematic Quantities Tells us how far something travels along a path = distance or change-in distance A B

Famous Kinematic Quantities Tells us how far something travels along a path = distance or change-in distance A B Does depend on path taken

Famous Kinematic Quantities Tells us how far something travels along a path = distance or change-in distance A B d or Δd Does depend on path taken

Famous Kinematic Quantities Tells us the straight-line distance and direction from start to finish. A B d or Δd

Famous Kinematic Quantities Tells us the straight-line distance and direction from start to finish. “ Displacement” A B d or Δd

Famous Kinematic Quantities Tells us the straight-line distance and direction from start to finish. “ Displacement” A B d or Δd Does not depend on path taken, only start and finish

Famous Kinematic Quantities Tells us the straight-line distance and direction from start to finish. “ Displacement” A B d or Δd Does not depend on path taken, only start and finish Δd

Famous Kinematic Quantities Tells us the straight-line distance and direction from start to finish. “ Displacement” A B d or Δd Does not depend on path taken, only start and finish Δd Definition of displacement: change of position

More Kinematics Quantities Tells us where something is relative to some given reference point

More Kinematics Quantities Tells us where something is relative to some given reference point Position

More Kinematics Quantities Tells us where something is relative to some given reference point Position Definition: straight line distance and direction of something relative to a reference point

More Kinematics Quantities Tells us where something is relative to some given reference point Position Definition: straight line distance and direction of something relative to a reference point Symbol: ???

More Kinematics Quantities Tells us where something is relative to some given reference point Position Definition: straight line distance and direction of something relative to a reference point Symbol: d

Position Example State the position of the stick man relative to the school. School N E 32º 53 m d =??

Position Example State the position of the stick man relative to the school. School N E 32º 53 m d = 53 m [E32°S] or [S58°E]

Comparison of Position and Displacement Position Displacement

Comparison of Position and Displacement Position vector Displacement vector

Comparison of Position and Displacement Position vector Straight line distance and direction of something from a given reference point Displacement vector

Comparison of Position and Displacement Position vector Straight line distance and direction of something from a given reference point Displacement vector Straight line distance and direction from a starting position to a finishing position

Comparison of Position and Displacement Position vector Straight line distance and direction of something from a given reference point Involves where something is at one instant in time Displacement vector Straight line distance and direction from a starting position to a finishing position

Comparison of Position and Displacement Position vector Straight line distance and direction of something from a given reference point Involves where something is at one instant in time Displacement vector Straight line distance and direction from a starting position to a finishing position Involves a definite interval of time with a starting time and a separate finishing time

Speed Definition: ????

Speed Definition: rate of change of distance or change- in distance over change-in time

Speed Definition: rate of change of distance or change- in distance over change-in time Defining Equation: ?????

Speed Definition: rate of change of distance or change- in distance over change-in time Defining Equation: V = Δd/Δt Symbol for speed

Speed Definition: rate of change of distance or change- in distance over change-in time Defining Equation: Units: ????? V = Δd/Δt Symbol for speed

Speed Definition: rate of change of distance or change- in distance over change-in time Defining Equation: Units: m/s km/h miles/h cm/s V = Δd/Δt Symbol for speed

Two kinds of Speed: Average and Instantaneous Average SpeedInstantaneous Speed

Two kinds of Speed: Average and Instantaneous Average Speed Use formula v=Δd/Δt Instantaneous Speed Use formula v=Δd/Δt

Two kinds of Speed: Average and Instantaneous Average Speed Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Instantaneous Speed Use formula v=Δd/Δt

Two kinds of Speed: Average and Instantaneous Average Speed Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Instantaneous Speed Use formula v=Δd/Δt Δt = t 2 -t 1 is so small that the initial time t 1 is infinitesimally close to t 2, therefore v ins occurs at one instant t 1 = t 2 = t

Two kinds of Speed: Average and Instantaneous Average Speed Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Slope of secant line of d vs t graph Instantaneous Speed Use formula v=Δd/Δt Δt = t 2 -t 1 is so small that the initial time t 1 is infinitesimally close to t 2, therefore v ins occurs at one instant t 1 = t 2 = t

Two kinds of Speed: Average and Instantaneous Average Speed Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Slope of secant line of d vs t graph Instantaneous Speed Use formula v=Δd/Δt Δt = t 2 -t 1 is so small that the initial time t 1 is infinitesimally close to t 2, therefore v ins occurs at one instant t 1 = t 2 = t Slope of tangent line of d vs t graph

Velocity Definition: ????

Velocity Definition: rate of change of position or change-in position over change-in time

Velocity Definition: rate of change of position or change-in position over change-in time Defining Equation: ????

Velocity Definition: rate of change of position or change-in position over change-in time Defining Equation: V = Δd/Δt velocity Change-in position or displacement

Velocity Definition: rate of change of position or change-in position over change-in time Defining Equation: V = Δd/Δt Units: ????? velocity Change-in position or displacement

Velocity Definition: rate of change of position or change-in position over change-in time Defining Equation: V = Δd/Δt Units: m/s km/h m/s cm/min velocity Change-in position or displacement

Two kinds of Velocity: Average and Instantaneous Average Velocity Instantaneous Velocity

Two kinds of Velocity: Average and Instantaneous Average Velocity Use formula v=Δd/Δt Instantaneous Velocity Use formula v=Δd/Δt

Two kinds of Velocity: Average and Instantaneous Average Velocity Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Instantaneous Velocity Use formula v=Δd/Δt

Two kinds of Velocity: Average and Instantaneous Average Velocity Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Instantaneous Velocity Use formula v=Δd/Δt Δt = t 2 -t 1 is so small that the initial time t 1 is infinitesimally close to t 2, therefore v ins occurs at one instant t 1 = t 2 = t

Two kinds of Velocity: Average and Instantaneous Average Velocity Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Slope of secant line of d vs t graph Instantaneous Velocity Use formula v=Δd/Δt Δt = t 2 -t 1 is so small that the initial time t 1 is infinitesimally close to t 2, therefore v ins occurs at one instant t 1 = t 2 = t

Two kinds of Velocity: Average and Instantaneous Average Velocity Use formula v=Δd/Δt Always involves a definite time interval with a distinct initial time t 1 and distinct final time t 2 so Δt = t 2 -t 1 ≠ 0 Slope of secant line of d vs t graph Instantaneous Velocity Use formula v=Δd/Δt Δt = t 2 -t 1 is so small that the initial time t 1 is infinitesimally close to t 2, therefore v ins occurs at one instant t 1 = t 2 = t Slope of tangent line of d vs t graph

Acceleration Definition: ??????

Acceleration Definition: rate of change of velocity or change-in velocity over change-in time

Acceleration Definition: rate of change of velocity or change-in velocity over change-in time Defining Equation: ???????

Acceleration Definition: rate of change of velocity or change-in velocity over change-in time Defining Equation: a =Δv/Δt = ???? acceleration Change-in velocity

Acceleration Definition: rate of change of velocity or change-in velocity over change-in time Defining Equation: a =Δv/Δt = (v 2 – v 1 )/Δt acceleration Change-in velocity Final velocity Initial velocity

Acceleration Definition: rate of change of velocity or change-in velocity over change-in time Defining Equation: a =Δv/Δt = (v 2 – v 1 )/Δt equations can be used for constant, average and instantaneous accelerations acceleration Change-in velocity Final velocity Initial velocity

Acceleration Definition: rate of change of velocity or change-in velocity over change-in time Defining Equation: a =Δv/Δt = (v 2 – v 1 )/Δt equations can be used for constant, average and instantaneous accelerations Units: m/s/s or m/s 2 or (km/h)/s and more acceleration Change-in velocity Final velocity Initial velocity

Three forms or Ways to get Acceleration To get an acceleration, we need a change-in velocity. In what ways can the velocity vector change?

Three forms or Ways to get Acceleration To get an acceleration, we need a change-in velocity. In what ways can the velocity vector change? 1.Speeding up... velocity vector increases in length when acceleration vector is oriented in same direction as initial velocity v1v1 a

Three forms or Ways to get Acceleration To get an acceleration, we need a change-in velocity. In what ways can the velocity vector change? 1.Speeding up... velocity vector increases in length when acceleration vector is oriented in same direction as initial velocity 2.Deceleration... Velocity vector decreases in length when acceleration vector is opposite direction as v 1 (slowing down) v1v1 a v1v1 a

Three forms or Ways to get Acceleration To get an acceleration, we need a change-in velocity. In what ways can the velocity vector change? 3.Changing direction... velocity vector changes direction but not magnitude or length when the acceleration vector is 90° to the initial velocity v1v1 a

Three forms or Ways to get Acceleration To get an acceleration, we need a change-in velocity. In what ways can the velocity vector change? 3.Changing direction... velocity vector changes direction but not magnitude or length when the acceleration vector is 90° to the initial velocity v1v1 a

Constant Acceleration

If the velocity changes by the same amount during equal time intervals

Constant Acceleration If the velocity changes by the same amount during equal time intervals Example: acceleration of projectiles near the earth's surface where air friction is negligible

Constant Acceleration If the velocity changes by the same amount during equal time intervals Example: acceleration of projectiles near the earth's surface where air friction is negligible a g = g = 9.80 m/s 2 [down] or ≈ 10.0 m/s 2 [down]

Constant Acceleration If the velocity changes by the same amount during equal time intervals Example: acceleration of projectiles near the earth's surface where air friction is negligible a g = g = 9.80 m/s 2 [down] or ≈ 10.0 m/s 2 [down] Meaning: ????????

Constant Acceleration If the velocity changes by the same amount during equal time intervals Example: acceleration of projectiles near the earth's surface where air friction is negligible a g = g = 9.80 m/s 2 [down] or ≈ 10.0 m/s 2 [down] Meaning: Every second, the velocity changes by 10.0 m/s [down]

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] ?

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up]

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] ?

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up]

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up] ?

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up] 0.00

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up] 0.00 ?

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up] [down]

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up] [down] ?

Constant Acceleration Example: projectile fired upward at 30.0 m/s Time (seconds) Instantaneous Velocity (meters/second) 30.0 [up] 20.0 [up] 10.0 [up] [down] 20.0 [down]

Deriving the Big Five Constant Acceleration Formulas

(1) Acceleration in terms of v 1, v 2 and Δt: a = ????

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) Δt

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) We will call this BIG FIVE #1a Δt

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) We will call this BIG FIVE #1a Δt Multiply both sides of #1a by Δt :

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) We will call this BIG FIVE #1a Δt Multiply both sides of #1a by Δt : Δt a = (v 2 - v 1 )

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) We will call this BIG FIVE #1a Δt Multiply both sides of #1a by Δt : Δt a = (v 2 - v 1 ) Divide both sides by a :

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) We will call this BIG FIVE #1a Δt Multiply both sides of #1a by Δt : Δt a = (v 2 - v 1 ) Divide both sides by a : Δt = (v 2 - v 1 ) a

Deriving the Big Five Constant Acceleration Formulas (1) Acceleration in terms of v 1, v 2 and Δt: a = (v 2 - v 1 ) We will call this BIG FIVE #1a Δt Multiply both sides of #1a by Δt : Δt a = (v 2 - v 1 ) Divide both sides by a : Δt = (v 2 - v 1 ) We will call this BIG FIVE #1b a

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt:

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt: From the previous slide we have: Δt a = (v 2 - v 1 )

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt: From the previous slide we have: Δt a = (v 2 - v 1 ) Reverse left and right sides: (mathematically legal)

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt: From the previous slide we have: Δt a = (v 2 - v 1 ) Reverse left and right sides: (mathematically legal) v 2 - v 1 = Δt a

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt: From the previous slide we have: Δt a = (v 2 - v 1 ) Reverse left and right sides: (mathematically legal) v 2 - v 1 = Δt a Solve for v 2

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt: From the previous slide we have: Δt a = (v 2 - v 1 ) Reverse left and right sides: (mathematically legal) v 2 - v 1 = Δt a Solve for v 2 v 2 = v 1 + Δt a

Deriving the Big Five Constant Acceleration Formulas (1) One more formula with acceleration in terms of v 1, v 2 and Δt: From the previous slide we have: Δt a = (v 2 - v 1 ) Reverse left and right sides: (mathematically legal) v 2 - v 1 = Δt a Solve for v 2 v 2 = v 1 + Δt a We will call this BIG FIVE #1c

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt:

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ?

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt Why can't this formula be used for acceleration ≠ 0 ?

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt Why can't this formula be used for acceleration ≠ 0 ? The above formula can be modified for a ≠ 0. How?

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt Why can't this formula be used for acceleration ≠ 0 ? The above formula can be modified for a ≠ 0. How? Δd = v avg Δt

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt Why can't this formula be used for acceleration ≠ 0 ? The above formula can be modified for a ≠ 0. How? Δd = v avg Δt What is v avg in terms of v 1 and v 2 ?

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt Why can't this formula be used for acceleration ≠ 0 ? The above formula can be modified for a ≠ 0. How? Δd = v avg Δt What is v avg in terms of v 1 and v 2 ? Δd = (v 1 + v 2 ) Δt 2

Deriving the Big Five Constant Acceleration Formulas (2) Displacement Δd in terms of v 1, v 2, and Δt: If an object moves at a constant velocity v for Δt, what formula gives us Δd ? Δd = v Δt Why can't this formula be used for acceleration ≠ 0 ? The above formula can be modified for a ≠ 0. How? Δd = v avg Δt What is v avg in terms of v 1 and v 2 ? Δd = (v 1 + v 2 ) Δt We will call this BIG FIVE #2 2

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2:

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2 Without simplifying, substitute #1c into #2:

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2 Without simplifying, substitute #1c into #2: Δd = (v 1 + v 1 + Δt a ) Δt 2

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2 Without simplifying, substitute #1c into #2: Δd = (v 1 + v 1 + Δt a ) Δt ?????? 2

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2 Without simplifying, substitute #1c into #2: Δd = (v 1 + v 1 + Δt a ) Δt Δd = (2v 1 + Δt a ) Δt 2 2

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2 Without simplifying, substitute #1c into #2: Δd = (v 1 + v 1 + Δt a ) Δt Δd = (2v 1 + Δt a ) Δt 2 2 Expand and simplify:

Deriving the Big Five Constant Acceleration Formulas (3) Displacement Δd in terms of v 1, Δt and a Here are BIG FIVE equations #1c and #2: v 2 = v 1 + Δt a #1c Δd = (v 1 + v 2 ) Δt #2 2 Without simplifying, substitute #1c into #2: Δd = (v 1 + v 1 + Δt a ) Δt Δd = (2v 1 + Δt a ) Δt 2 2 Expand and simplify: Δd = v 1 Δt + a Δt 2 /2 We will call this BIG FIVE equation #3

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2 Substitute #1b into #2 ???????

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2 Substitute #1b into #2 Δd = (v 1 + v 2 )(v 2 - v 1 ) 2 a

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2 Substitute #1b into #2 Δd = (v 1 + v 2 )(v 2 - v 1 ) Δd = (v 2 + v 1 )(v 2 - v 1 ) 2 a 2 a

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2 Substitute #1b into #2 Δd = (v 1 + v 2 )(v 2 - v 1 ) Δd = (v 2 + v 1 )(v 2 - v 1 ) 2 a 2 a

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2 Substitute #1b into #2 Δd = (v 1 + v 2 )(v 2 - v 1 ) Δd = (v 2 + v 1 )(v 2 - v 1 ) 2 a 2 a Δd = (v 2 2 – v 1 2 ) 2 a

Deriving the Big Five Constant Acceleration Formulas (4) Displacement Δd in terms of v 1, v 2 and a Here are BIG FIVE equations #1b and #2: Δt = (v 2 - v 1 ) #1b Δd = (v 1 + v 2 ) Δt #2 a 2 Substitute #1b into #2 Δd = (v 1 + v 2 )(v 2 - v 1 ) Δd = (v 2 + v 1 )(v 2 - v 1 ) 2 a 2 a Δd = (v 2 2 – v 1 2 ) 2 a We will call this BIG FIVE Equation #4

Big Five equation #5 Homework Exercise: Derive the fifth Big Five equation using one form equation #1 and equation #2. This equation is: Δ d = v 2 Δt - a Δt 2 /2

List of BIG FIVE equations Memorize these please!! (#1a) a = (v 2 - v 1 ) (#1b) Δt = (v 2 - v 1 ) Δt a (#1c) v 2 = v 1 + Δt a (#2) Δd = (v 1 + v 2 ) Δt (#3) Δd = v 1 Δt + a Δt 2 /2 2 (#4) Δd = (v 2 2 – v 1 2 ) or (#4b) v 2 2 – v 1 2 = 2aΔd 2a (#5) Δ d = v 2 Δt - a Δt 2 /2

When can we use the BIG FIVE? Only for constant non-zero acceleration

When can we use the BIG FIVE? Only for constant non-zero acceleration Note: Vector quantities cannot be multiplied together. Some of the BIG FIVE equations appear to break this rule. However, if the motion analyzed is along a line in one dimension, we can get away with multiplying vectors by representing them as + or – integers.

When can we use the BIG FIVE? Only for constant non-zero acceleration Note: Vector quantities cannot be multiplied together. Some of the BIG FIVE equations appear to break this rule. However, if the motion analyzed is along a line in one dimension, we can get away with multiplying vectors by representing them as + or – integers. Example: 2aΔd = 2(10.0 m/s 2 [down])(2.5 m [up]) = ?????

When can we use the BIG FIVE? Only for constant non-zero acceleration Note: Vector quantities cannot be multiplied together. Some of the BIG FIVE equations appear to break this rule. However, if the motion analyzed is along a line in one dimension, we can get away with multiplying vectors by representing them as + or – integers. Example: 2aΔd = 2(10.0 m/s 2 [down])(2.5 m [up]) = 2(-10)(+2.5)

When can we use the BIG FIVE? Only for constant non-zero acceleration Note: Vector quantities cannot be multiplied together. Some of the BIG FIVE equations appear to break this rule. However, if the motion analyzed is along a line in one dimension, we can get away with multiplying vectors by representing them as + or – integers. Example: 2aΔd = 2(10.0 m/s 2 [down])(2.5 m [up]) = 2(-10)(+2.5) = -50 = ?????

When can we use the BIG FIVE? Only for constant non-zero acceleration Note: Vector quantities cannot be multiplied together. Some of the BIG FIVE equations appear to break this rule. However, if the motion analyzed is along a line in one dimension, we can get away with multiplying vectors by representing them as + or – integers. Example: 2aΔd = 2(10.0 m/s 2 [down])(2.5 m [up]) = 2(-10)(+2.5) = -50 = 50 m 2 /s 2 [down]

What equations do we use for a =0 ?

If the acceleration is zero, how do we describe the motion?

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ?

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ? Δd = v Δt

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ? Δd = v Δt This is called the LITTLE ONE!!

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ? Δd = v Δt Note there are two other forms of this same equation. What are they?

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ? Δd = v Δt Note there are two other forms of this same equation. What are they? Δt = Δd/v and v = Δd/Δt

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ? Δd = v Δt Note there are two other forms of this same equation. What are they? Δt = Δd/v and v = Δd/Δt Δd v Δt

What equations do we use for a =0 ? If the acceleration is zero, how do we describe the motion? a =0 means constant velocity There is only one equation that describes motion at a constant velocity. What is it ? Δd = v Δt Note there are two other forms of this same equation. What are they? Δt = Δd/v and v = Δd/ΔtΔd Again we call this the LITTLE one! v Δt