1. Change in velocity with time
Acceleration
Change in velocity with time

2. Acceleration: Change in velocity with time.
Acceleration may be calculated as the
Increase in velocity—objects speed up
Decrease in velocity—objects slow down
Change in direction
Change in “how fast” and direction.

4. The cyclist is accelerating because his velocity is changing
The cyclist is accelerating because his velocity is changing. He is moving faster each second he ride.

5. If the object’s velocity is not changing (constant velocity), acceleration is ZERO.
10 m/s
10 m/s
10 m/s
10 m/s
The car is not getting faster.
The car is not getting slower.
The car is not changing direction.
Velocity remains constant.

6. 10 m/s
Velocity is not changing. Car is moving at 10 m/s. Zero acceleration.

7. If the object is getting faster (speeding up), acceleration is in the same direction as the object’s motion.
2 m/s
4 m/s
6m/s
8 m/s
The car’s velocity is increasing per second.
The force causing the acceleration is in the same direction as the car’s motion.
Velocity and acceleration are the same sign (+ and +, or - and -)

8. 2 m/s
4 m/s
6m/s
8 m/s
Velocity is increasing from 2 m/s to 8 m/s. Car is accelerating as it gets faster.

9. If the object is getting slower (slowing down), acceleration is in opposite direction of the object’s motion.
8 m/s
6 m/s
4 m/s
2 m/s
The car’s velocity is decreasing per second.
The force causing the acceleration is in the opposite direction as the car’s motion.
Velocity and acceleration are different signs (+ and -, or - and +)

10. 2 m/s
4 m/s
6 m/s
8 m/s
Velocity is decreasing from 8 m/s to 2 m/s. Car is accelerating as it gets slower.

11. Centripetal acceleration is the constant change in velocity as an object changes direction.
Velocity (a vector) changes if direction changes. This is true even if the magnitude (“how fast”) remains constant.
The bicyclist and the car are changing direction, thus they are accelerating.

12. Identify the direction of the acceleration.
Car moves east, slowing down
Car moves south, speeding up.
Car moves north, speeding up.
Car moves left, slowing down.
Car moves right, speeding up.
Car moves south, slowing down.
Car moves west, speeding up.

13. Identify the direction of the acceleration.
Car moves east, slowing down (WEST)
Car moves south, speeding up. (SOUTH)
Car moves north, speeding up. (NORTH)
Car moves left, slowing down. (RIGHT)
Car moves right, speeding up. (RIGHT)
Car moves south, slowing down. (NORTH)
Car moves west, speeding up. (WEST)

14. Identify the direction of the acceleration.
Car’s velocity 0 m/s to 20 m/s north.
Car’s velocity -5 m/s to -20 m/s south.
Car’s velocity -25 m/s to -10 m/s west.
Car’s velocity 25 m/s to 25 m/s east
Car’s velocity 30 m/s to 0 m/s east
Car’s velocity 15 m/s to 15 m/s north
Car’s velocity -10 m/s to -30 m/s west

15. Identify the direction of the acceleration.
Car’s velocity 0 m/s to 20 m/s north. (NORTH)
Car’s velocity -5 m/s to -20 m/s south. (SOUTH)
Car’s velocity -25 m/s to -10 m/s west. (EAST)
Car’s velocity 25 m/s to 25 m/s east (ZERO)
Car’s velocity 30 m/s to 0 m/s east (WEST)
Car’s velocity 15 m/s to 15 m/s north (ZERO)
Car’s velocity -10 m/s to -30 m/s west (WEST)

16. The value of acceleration describes how the magnitude of velocity changes for every second an object gets faster or gets slower.
Suppose an object undergoes acceleration of 2.0 m/s2.
What happens? For every 1 second the object moves, the velocity will change by 2.0 m/s.
Suppose an object undergoes acceleration of -3.0 m/s2.
What happens? For every 1 second the object moves, the velocity will change by -3.0 m/s.

17. Concept Review
Question: What is acceleration?
Question: What are the four ways that an object can accelerate?
Question: Under what circumstances would an object have an acceleration of zero?

18. Calculating Acceleration
Acceleration has the units: m/s2.
Use this equation if you know the initial and the final velocity.
= initial velocity (m/s)
= final velocity (m/s)
t = time for object to accelerate (s)

19. Calculating Acceleration
Acceleration has the units: m/s2.
Use this equation if you know the initial velocity and the change in position.
x = “distance” of acceleration (m)
t = time for object to accelerate (s)
v = initial velocity

20. = initial velocity (m/s) = final velocity (m/s)
How fast an object moves after acceleration is complete: Solving for the final velocity.
= initial velocity (m/s)
= final velocity (m/s)
t = time for object to accelerate (s)
a = acceleration (m/s)

21. x = “distance” of acceleration (m) = initial velocity (m/s)
“How far” an object moved during acceleration: Solving for the “distance”.
x = “distance” of acceleration (m)
= initial velocity (m/s)
t = time for object to accelerate (s)
a = acceleration (m/s)

22. A car is moving at an initial velocity of 5. 0 m/s E
A car is moving at an initial velocity of 5.0 m/s E. The car accelerates to 15 m/s E in 9 seconds.
Calculate the acceleration of the car.
Calculate how far the car moved as it accelerated.
9 s
5 m/s
15 m/s

23. Starting velocity = 5 m/s E
Final velocity = 15 m/s E
Time = 9 s

24. A car on the freeway slows from 30 m/s N to 20 m/s N in 15 seconds.
Calculate the acceleration of the car.
Calculate how far the car moved as it accelerated.
15 s
30 m/s
20 m/s

25. Starting velocity = 30 m/s N
Final velocity = 20 m/s N
Time = 15 s

26. From a stop, the racecar accelerates over a distance of 300 meters in 9 seconds.
Calculate the acceleration of the car.
Calculate how fast was it moving after it accelerated.
300 m; 9.0 s

27. Starting velocity = 30 m/s N
Final velocity = 20 m/s N
Time = 15 s

28. From an initial velocity of 10 m/s N, the racecar gets faster over a distance of 300 meters in 9 seconds.
Calculate the acceleration of the car.
Calculate how fast was the car moving after it accelerated.
300 m; 9.0 s

29. Starting velocity = 10 m/s N
Time = 9 s
Displacement = 300 m

30. Concept Review
What is acceleration?
What are the four ways that an object can accelerate?
Explain the meaning of acceleration with regard to velocity changes.

31. Predict the direction of acceleration
From -25 m/s to -30 m/s south.
From 15 m/s to 5 m/s east.
Moving west and getting faster.
Moving left and getting slower.
10 m/s to 20 m/s north
Flying upward and getting slower
Falling and getting faster

32. Starting from 5. 0 m/s, the car accelerates at 1
Starting from 5.0 m/s, the car accelerates at 1.20 m/s2 for 20 seconds.
Calculate how far the car moved.
Calculate the final velocity of the car.
A car accelerates from 40 m/s to 20 m/s in 6 second.
Calculate the acceleration of the car.

33. Starting from 5.0 m/s, the got faster over a distance of 150 m for 10 seconds.
Calculate the acceleration of the car.
Calculate the final velocity of the car.
A car had an acceleration of 1.67 m/s2. It accelerated 8 seconds starting from 10 m/s.
Calculate how far the car moved.

34. Starting from 5. 0 m/s, the car accelerates at 1
Starting from 5.0 m/s, the car accelerates at 1.20 m/s2 for 20 seconds.
Calculate “how far” the car moved during acceleration.
Calculate the final velocity of the car.
5.0 m/s
1.20 m/s2, 20 s
Car is moving east, velocity is positive. Acceleration is positive, east. Because acceleration is in the same direction, the car will get faster.

35. 5.0 m/s
1.20 m/s2, 20 s
“How far”
Final velocity

36. Starting from -25 m/s, the car accelerates at 0.80 m/s2 for 12 seconds.
Calculate “how far” the car moved during acceleration.
Calculate the final velocity of the car.
-25.0 m/s
0.80 m/s2, 12 s
Car is moving west, velocity is negative. Acceleration is positive, east. Because acceleration is in the opposite direction, the car will slow down.

37. -25.0 m/s
0.80 m/s2, 12 s
“How far”
Final velocity