1. Acceleration

2. Change in Velocity Each time you take a step you
are changing your velocity.
You are probably most familiar with the velocity changes of a moving bus or car.
The rate at which velocity (speed or direction) changes is called acceleration.

3. Acceleration Acceleration is a change is speed or in direction.
“Change in” can be denoted by the Greek letter delta (Δ), so change in speed can be written ΔS and read as “delta s”, or “change in speed”.
Math term!
Change in speed is final speed minus initial speed
∆s = Sf – Si

4. So acceleration= change in velocity or a = ∆v time t
Acceleration= final velocity- starting velocity
time
If change in velocity =
final velocity – starting velocity
So acceleration= change in velocity or a = ∆v
time t

5. To find acceleration, we need to know:
1. Change in speed:
The bicycle went
from a stop to 20 mph.
∆S = 20 – 0 = 20mph
2. The time the change
took: It took the bicyclist
5 seconds
t = 5 sec

6. Change in speed = 20 mph – 0 mph or 4 m/h/s
Time sec
or each second the bike increases its speed 4 m/h.
*NOTE: The acceleration label has 3 units:
a speed (m/h) and a time (s).
Commonly, the units are m/s/s or m/s2 but they can be mi/h/s
OR mi/h/h
OR km/h/min
OR k/h/s
OR m/s/min
any unit that has both a speed and a time.

7. Acceleration
3 Types of Acceleration
Speeding Up
Slowing Down
Turning

8. Positive acceleration Negative acceleration

9. Here is an example of acceleration
At time: Speed is: Total distance traveled
0 s 0 m/s 0 m
1 s 5 m/s 5 m
2 s 10 m/s 15 m
3 s 15 m/s 30 m
4 s 20 m/s 50 m
5 s 25 m/s 75 m
This object is gaining 5 m/s of speed every second.
Speed could be graphed as a straight line with a slope of 5 m/s.
Note the total distance it travels goes up and would be graphed as a curve.

10. Speed 70 60 50 40 30 20 10
Distance
Seconds

11. Distance Traveled Seconds Total Distance 70 60 50 40 30 20 10
Seconds

12. Deceleration Deceleration is slowing down.
Sometimes it is called negative acceleration.
0 m/h – 25 m/h = -25 m/h

13. EXAMPLE: A car traveling at 60 mph accelerates to 90 mph in 3 seconds.
What is the car’s acceleration?
Velocity(final) - Velocity(original)
Acceleration =
time
90 mph - 60 mph =
3 seconds
30 mph =
3 seconds =
10 mph/second

14. EXAMPLE: A car traveling at 60 mph slams on the
brakes to avoid hitting a deer. The car comes to a
stop 6 seconds after applying the brakes. What is
The car’s acceleration?
Velocity(final) - Velocity(original)
Acceleration =
time
0 mph - 60 mph =
6 seconds
- 60 mph =
6 seconds =
- 10 miles per hour per second

15. How can a car be accelerating if its speed is a constant 65 km/h?
Question
How can a car be accelerating if its speed is a constant 65 km/h?

16. If the car is changing directions, it is accelerating.
Answer
If the car is changing directions, it is accelerating.

17. Constant acceleration graphs as a straight line or linear slope (rise/run).

18. The slope of a non-linear velocity-time graph (rise/run) can show an object’s motion.

19. Graphing Acceleration: Speed vs. Time Graphs
On a Speed vs. Time graph
Speed is increasing with time = accelerating
Line is straight = acceleration is constant

20. Graphing Acceleration: Distance vs. Time Graphs
1) distance is increasing with time.
2) line is curved = speed is increasing.
Remember slope = speed.

21. Question: Which line represents an object that is accelerating?
The black and red lines represent objects that are accelerating.
The black line shows an object going a greater distance each second, so it must be speeding up.
The red line shows an object is going less far each second, so must be slowing down.
Remember: in distance vs. time graphs:
curved line = accelerating flat line = constant speed
Which line represents an object that is accelerating?

22. Question The car is slowing down
Run = 6 s
Rise = -12 m/s
Above is a graph showing the speed of a car over time.
1) How is the speed of the car changing (is it speeding up,
slowing down, or staying the same)?
2) What is this car’s acceleration?
The car is slowing down
Acceleration = rise/run = -12m/s ÷6s = -2 m/s2

23. Galileo Galilei Lived 1564 - 1642
He studied how things fell, but didn’t have a good clock
He rolled balls down an inclined plane, and found that the speed increased as the ball rolled down the ramp

24. Galileo Acceleration= change in velocity time t = 0 t = 1 second
t = 2 seconds
t = 3 seconds

25. Galileo
Galileo found that the same things happen over & over when things fall. But he didn’t drop things from Tower of Pisa, as is often heard.
Object falling goes a different distance each second, at first

26. Falling Air resistance will increase as an object falls faster.
Air resistance is an upward force on the object.
Eventually gravity will balance with air resistance.
At that point, the object reaches terminal velocity - highest speed reached by a falling object.

27. Free fall
The constant acceleration of an object moving only under the force of gravity is "g".
The acceleration caused by gravity is 9.8 m/s2
If there was no air, all objects would fall at the same speed
Doesn’t depend on mass
After 1 second falling at 10 m/s
After 2 seconds 20 m/s
3 seconds 30 m/s

28. Terminal velocity The force of gravity is constant
Air resistance increases as you speed up until the force is equal to the force of gravity
Equal forces = no acceleration
This means terminal velocity is a constant velocity