One Dimensional Motion

How far something has moved Distance How far something has moved

Distance Scalar quantity

How far something is from its starting position Displacement How far something is from its starting position

Displacement A vector quantity

The interval between two occurrences Time The interval between two occurrences

Equal displacement occurs during successive equal time intervals Uniform Motion Equal displacement occurs during successive equal time intervals

Velocity is constant during uniform motion

Distance vs Time Graph

Slope Slope = rise/run Slope = Dy/Dx

Slope On a distance vs time graph: Slope = Dd/Dt

Slope Slope = Dd/Dt Slope = velocity

Average Velocity v = Dd/Dt v = d1 – d0 t1 – t0

Displacement df = di + vti d = di + vt

Distance vs Time Graph

Distance vs Time Graph

Acceleration a = Dv/Dt a = vf - vi tf - ti

Velocity v = v0 + at vf = vi + at

Displacement d = di + vit + ½ at2

Displacement df = di + vit + ½ at2

v2 = vi2 + 2 a(df – di) v2 = vi2 + 2ad

vf2 = vi2 + 2ad

v = v0 + at d = d0 + v0t + ½ at2 v2 = v02 + 2ad

v = v0 + at vf = vi + at

d = d0 + v0t + ½ at2 df = di + vit + ½ at2

df = di + vit + ½ at2 d = vit + ½ at2

v2 = v02 + 2ad vf2 = vi2 + 2ad

vf = vi + at d = vit + ½ at2 vf2 = vi2+ 2ad

A ball is dropped from 490 m. Calculate its: Drill A ball is dropped from 490 m. Calculate its: vf & tair

A car starts 200. 0 m west of town, and moves at 15 m/s east A car starts 200.0 m west of town, and moves at 15 m/s east. 1) write its best equation 2) where will the car be at 10.0 s 3) When will the car be in town

Determining Instantaneous Velocity Graph the Dd/Dt data Draw tangent to point of interest Determine slope of tangent

Velocity vs Time Graphs

a = slope d = xy or vt d = area

a = slope = Dy/Dx = Dv/Dt = 62/5 = 12.4 m/s2

d = area under curve

Define each of the following Distance Displacement Speed Velocity Acceleration

Describe the motion for each series

Drill: The velocity of a car is increased from 25 to 75 m/s west in 10.0 s. Calculate: a & d

vf = vi + at d = vit + ½ at2 vf2 = vi2+ 2ad

Describe the motion between each interval

Describe the motion of each series

Draw a position time graph for a person who walks uniformly from the positive side of the origin back thru the origin to the negative side. Repeat for the negative side.

Make the following conversions: a) 10 m/s to km/hr b) 72 mph to m/s 1.6 km/mile

Draw a position time graph of a person who walks one block briskly, waits at a traffic light, walks the next block slowly, waits at another light, then runs the last block.

A truck starts 400.0 m east of town, and moves at 12 m/s west Find the time & place where the car from the last problem & the truck will be at the same place

A car increases its velocity from 4.0 m/s to 36 m/s over 4.0 s. Calculate: a & d

The same car slows from 36 m/s to 15 m/s in 3.0 s. 1) Calculate the average acceleration & dis

A car accelerates from 15 m/s to 25 m/s in 125 m. Calculate its time & acceleration

Drill:A car is coasting backwards at 3. 0 m/s when its engine starts Drill:A car is coasting backwards at 3.0 m/s when its engine starts. After 2.5 s the car is going 4.5 m/s. Calculate a & d

Motion Variables: vi vf a t d

Make a chart like the one to the right vi vf a t d

A car going 4.0 m/s accelerates at 3.0 m/s2 for 4.0 s. Calculate: vf & d

A car slows from 44 m/s to 22 m/s in 11 s. Calculate: a & d

Motion Affected by Gravity

A force of attraction between two masses Gravity A force of attraction between two masses

This force causes objects to accelerate towards each other Gravity This force causes objects to accelerate towards each other

Gravity The acceleration of gravity is relatively constant over the Earth’s surface

Acceleration of Gravity (ag or g) 9.81 m/s2 Down or (-)

Any object in air will have a vertical acceleration of Gravity Any object in air will have a vertical acceleration of -9.81 m/s2

A ball is dropped from a 0. 49 km cliff A ball is dropped from a 0.49 km cliff. The acceleration of gravity is -9.8 m/s2. Calculate: vmax & t

HW: A ball is thrown straight up at 19. 6 m/s HW: A ball is thrown straight up at 19.6 m/s. The acceleration of gravity is -9.8 m/s2. Calculate: hmax & tair

Drill: A ball is dropped from a ledge & lands 8.0 s later. Calculate: hledge & vmax

Homework Problems: 27 – 30 Page 103

Drill A ball drops from 0.49 km. Calculate: tair & vmax

Calculate its tair, vf, & hmax A man on the ground shoots a gun straight up & the bullet exits the barrel at 980 m/s. The acceleration of gravity is -9.8 m/s2. Calculate its tair, vf, & hmax

A ball was dropped & landed at 70. 0 m/s A ball was dropped & landed at 70.0 m/s. The acceleration of gravity is -9.8 m/s2. Calculate: d & tair

A pumpkin was dropped from a plane & stayed in air for 10. 0 s A pumpkin was dropped from a plane & stayed in air for 10.0 s. The acceleration of gravity is -9.81 m/s2. Calculate: h & vmax.

Homework Problems: 31 - 33 Page 106

Calculate its tair, vf, & hmax A cannon on a 2500 m cliff is fired straight up & the ball exits the barrel at 0.98 km/s. The acceleration of gravity is -9.8 m/s2. Calculate its tair, vf, & hmax

A ball is shot straight up to a height of 1. 96 km A ball is shot straight up to a height of 1.96 km. The acceleration of gravity is -9.8 m/s2. Calculate: tair & vi

Drill: A car increases its velocity from 36 km/hr to 72 km/hr in 5.0 s. Calculate: a & d

A car rolling backwards at 5.0 m/s accelerates at 3.0 m/s2 for 4.0 s. Calculate: vfinal & d

A car rolling backwards at 25. 0 m/s accelerates at 5. 0 m/s2 for 12 A car rolling backwards at 25.0 m/s accelerates at 5.0 m/s2 for 12.0 s. Calculate: vf & d

Homework Problems: 58 - 60 Page 112 & 113

Drill: A ball is thrown straight up at 9800 cm/s. Calculate: tair & hmax

A ball is thrown straight down at 25 m/s & stays in air for 4.0 s. g = -9.8 m/s2 Calculate: initial height & vf of the ball.

A ball is thrown straight up to a height of 49 m. g = -9.8 m/s2 Calculate: vi & tair

Homework Problems: 66 - 68 Page 114

Drill: A ball is thrown straight sideways & lands in 5. 0 s Drill: A ball is thrown straight sideways & lands in 5.0 s. Calculate: initial height & vmax down

Calculate: a & d during that time. A car rolling backwards at 5.0 m/s accelerates to 11 m/s forward in 4.0 s. Calculate: a & d during that time.

A car going 36 km/hr slams on brakes, but still hits a tree at 6 A car going 36 km/hr slams on brakes, but still hits a tree at 6.0 km/hr after 1.0 s. Calculate: a & d during that time.

Drill: A ball is thrown straight up and hits the ground in 6.0 sec. Calculate: hmax & vi

Test Date Wednesday 10/25/06

36 km/hr to 54 km/hr in 5.0 s. Calculate: a & d during that time. Drill: A car goes from 36 km/hr to 54 km/hr in 5.0 s. Calculate: a & d during that time.

Matching Stuff Formulas Definitions Units

Definitions Motion Position Velocity Speed Distance Displacement Time Acceleration

Units Displacement Time Velocity Acceleration

A ball is thrown straight up at 49 m/s. Calculate: tair & hmax

Calculate: a & d during that time. A car rolling backwards at 6.0 km/hr accelerates to 30.0 km/hr forward in 6.0 s. Calculate: a & d during that time.

A ball is thrown straight up to a height of 490 m. Calculate: tair & vi