9/23 do now – on a new sheet Which of the following is the expression for average velocity? Homework questions?

Motion in one dimension 2.2 Acceleration

Lesson Objectives: Describe motion in terms of changing velocity. Compare graphical representations of accelerated and nonaccelerated motions. Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

Do Now - Notes Key terms and ideas notes Acceleration def. Acceleration direction Graph representation Equations

Acceleration Acceleration Acceleration is a Vector quantity change in VELOCITY occuring over TIME Acceleration = (change in velocity) / time Acceleration is a Vector quantity The unit for acceleration is m/s2 Questions: “If an object has a large velocity, does it necessarily have a large acceleration? If an object has a large acceleration, does it necessarily have a large velocity?”

What are the three ways to accelerate your car? Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration. What are the three ways to accelerate your car? Gas pedal, break, steering wheel

Example – finding time of acceleration A shuttle bus slows to a stop with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to 0.0 m/s?

Example – finding time of acceleration Find the acceleration of an amusement park ride that falls from rest to a speed of 28 m/s in 3.0 s.

Do now In addition to displacement, which of the following must be used for a more complete description of the average velocity of an object? finish Class work Page 49 #1-5

The Direction of the Acceleration Vector Negative Velocity Negative Velocity Positive Velocity Positive Velocity Negative Acceleration Negative Acceleration Positive Acceleration Positive Acceleration Slowing down Eventually speeds up in + direction! Slowing down Eventually speeds up in – direction! Speeding up in + direction Speeding up in - direction

The Direction of the Acceleration Vector demo The Direction of the Acceleration Vector The direction of the acceleration vector depends on whether the object is speeding up or slowing down If an object is speeding up, then its acceleration is in the same direction of its motion. moving in the + direction, the acceleration + direction moving in the - direction, the acceleration - direction If an object is slowing down, then its acceleration is in the opposite direction of its motion. moving in the + direction, the acceleration - direction moving in the - direction, the acceleration + direction The direction of velocity and acceleration do not have to be the same!!!

The car will… The car will… The car will… The car will… +v -v +v -v +a Conceptual challenge Page 50

The slope of the v-t graph describe the object’s acceleration Figure 2-10 B C What is the Acceleration at A, B, C, D? A D A: +10 m/s2 B: zero C: -5 m/s2 D:-15 m/s2 What is happening at point D?

Conceptual challenge Page 50

Constant acceleration demo Constant acceleration - the velocity is changing by a constant amount - in each second of time.

= vf + vi 2 ∆x ∆t ∆x = ½ (∆t)(vf + vi) a = slope ∆x = ½ (∆t)(vf + vi) The displacement equals to the area under the velocity vs. time graph

Determining the Area on a v-t Graph In velocity versus time graphs, the area bounded by the line and the axes represents the displacement.

The shaded area is representative of the displacement area = base x height area = ½ base x height area = ½ base x ( height1 + height2) or area = big triangle – small triangle

example Determine the displacement of the object during the time interval from 2 to 3 seconds (Practice A) and during the first 2 seconds (Practice B). 25 m 40 m

Example – 2C A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and breaking system, and comes to rest 5.5 s later. Find how far the car moves before stopping. 120 m

Class work Page 53 – practice 2C

Do now Velocity measures all of the following EXCEPT a. the speed of an object. b. the total displacement of an object. c. the direction of an object’s motion. d. the displacement for each time interval.

Lesson Objectives: Describe motion in terms of changing velocity. Compare graphical representations of accelerated and nonaccelerated motions. Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration. Homework: Castle learning Must show work for incorrect answer after one try on a separate paper Show name of assignment

Constant motion vs. accelerated motion ticker tape constant velocity: displacement is changing by a constant amount - in each second of time. constant acceleration: displacement is increasing in each second of time. Velocity is changing by a constant amount - in each second of time

Constant motion vs. accelerated motion vector diagrams

When velocity is constant displacement vs. time (constant motion) displacement displacement time time Constant, positive velocity At rest Constant motion - constant speed with constant direction Slope represent velocity Alert: in displacement vs. time graph, displacement can be positive or negative

velocity vs. time (constant motion) Constant, positive velocity, zero acceleration Constant negative velocity, zero acceleration Slope represent acceleration Alert: in velocity vs. time graph, velocity can be positive or negative

When velocity is changing displacement vs. time (accelerated motion) displacement time displacement Slowing down in positive direction Speeding up in positive direction time displacement time displacement time Slowing down in negative direction Speeding up in negative direction

velocity vs. time (constant accelerated motion) Speeding up in positive direction at constant rate Acceleration is constant, positive Slowing down in positive direction at constant rate, acceleration is constant, negative velocity time velocity time velocity velocity time time Speeding up in negative direction at constant rate Acceleration is constant, negative Slowing down in negative direction at constant rate, acceleration is constant, positive

Alert – v vs. t and d vs. t must match velocity time Disp. time Disp. time velocity time velocity velocity time Disp. time Disp. time time

Determine acceleration - Example 1 From 0 s to 4 s: From 4 s to 8 s: 0 m/s2 2 m/s2

Do now Sketch displacement vs. time and velocity vs. time graphs to indicate an object is accelerating at a constant rate.

Lesson Objectives: Describe motion in terms of changing velocity. Compare graphical representations of accelerated and nonaccelerated motions. Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

review Key terms and ideas notes Acceleration def. Acceleration direction Graph representation Equations Speed up: a and v have same sign Slow down: a and v have opp. Sign acc. = slope disp = area v d v d vavg No acc. No acc. t t t t

Final velocity depends on initial velocity, acceleration, and time

v vf vi t tf In velocity versus time graphs, the area bounded by the line and the axes represents the displacement.

Example 2D A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff. What is the its speed at takeoff? How long must the runway be for the plane to be able to take off?

Class work Page 55, practice 2D

Time and be found from displacement and velocity Solve for ∆t Sub ∆t in this equation

Example – 2E A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. what is the velocity of the stroller after it has traveled 4.75 m?

Class work Page 58 – practice 2E #1-6

In one dimensional motion: ∆x = d

Class work Section Review Worksheet 2-2

Do now A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average speed and average velocity of the car during this 20.-second interval?

Describe motion in terms of changing velocity. Objectives - review Describe motion in terms of changing velocity. Compare graphical representations of accelerated and non accelerated motions. Apply kinematics equations to calculate distance, time, or velocity under conditions of constant acceleration. Homework Castle learning, must show work for incorrect answers to get full credit

In one dimensional motion: ∆x = d

Example A bicyclist accelerates from 5.0 m/s to a velocity of 16 m/s in 8 s. Assuming uniform acceleration, what displacement does the bicyclist travel during this time interval? ∆x = ½ (vf + vi)(∆t) 84 m

Example A train starts from rest and leaves Greenburg station and travels for 500. meters with an acceleration of 1.20 meters per second2. What is the train’s final velocity? How long does it take the train to reach its final velocity? vf2 = vi2 + 2ad vf2 = 0 + 2(1.20 m/s2)(500. m) vf = 34.6 m/s vf = vi + at 34.6 m/s = 0 + (1.20 m/s2) t t = 28.8 s

Example A driver traveling at 85. miles per hour sees a police car hiding in the trees 2.00 miles ahead. He applies his brakes, decelerating at -500. miles per hour2. If the speed limit is 55 mph, will he get a ticket? What would his acceleration need to be to not get a ticket? vf2 = vi2 + 2ad vf2 = (85. mph)2 + 2(-500. mph2)(2.00 mi) vf = 72.3 mph *YES* vf2 = vi2 + 2ad (55 mph)2 = (85. mph)2 + 2a(2.00 mi) a = -1050 mph2

Class work Problem workbook 2A, 2B, 2C, 2D, 2E