1. Unit 6 (2) Acceleration
Physical Science

2. Review video

3. Acceleration Acceleration rate of change in velocity
speeding up, slowing down, or changing direction.
It is a vector
Can be positive like a car speeding up
Can be negative, like a car breaking.
Acceleration and Deceleration are measured in meters per second per second, which is written m/s2 (how much velocity changes in a second)
Units: m/s/s or m/s2 , km/h/h or km/h2 , km/h/s

4. Acceleration a : acceleration Vf : final velocity
the rate of change of velocity
change in speed or direction
Δ is the Greek letter “delta” & means “change”
a : acceleration
Vf : final velocity
Vi : initial velocity
t : time

5. Change in direction Any time an object turns it has an acceleration
Even though the speed may be constant, the direction is changing
Constant acceleration is a steady change in velocity

6. Acceleration (cont.)
IF:
an object travels in a straight line, acceleration is just the rate of change of speed.
the acceleration is in the same direction as the velocity (change of direction), then the object speeds up.
the acceleration is in the opposite direction from velocity, then the object slows down.

7. Acceleration Key Points
Equation: a = Δv = vf - vi
Δt Δt
Key Phrases:
Starts “at rest” – initial velocity is zero
“Dropped” – initial velocity is zero
“Comes to a stop” – final velocity is zero
“What is the change in velocity?” – just solve for Δv.
f = final
i = initial

8. Acceleration
A certain car can go from 0 to 60 mi/hr in 5 seconds. What is the car’s acceleration?
What are we solving for?
The car’s acceleration, a.
a = (vf – vi) / t
a = (60 mi/hr – 0 mi/hr) / 5 s
a = (60 mi/hr) / 5 s
a = 12 mi/hr/s
For every second that passes, the car is going 12 mi/hr faster.
vf - vi t a

9. Acceleration
Acceleration can be negative if an object is slowing down.
A car is going 55 mi/hr when the driver slams on the brakes. The car stops in 4 seconds. What is the car’s acceleration?
What are we solving for?
The car’s acceleration, a.
a = (vf – vi) / t
a = (0 mi/hr – 55 mi/hr) / 4 s
a = (-55 mi/hr) / 4s
a = mi/hr/s
vf - vi t a

10. Acceleration due to gravity
Known as free fall
Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8m/s2

11. Acceleration Due to Gravity
Gravity causes an object to accelerate downward.
9.8 m/s/s
An object is dropped and falls for 4 seconds. How fast is it moving?
What are we solving for?
vf, the final velocity
a = (vf – vi) / t
9.8 m/s/s = (vf – 0 m/s) / 4 s
39.2 m/s = vf – 0 m/s
vf = 39.2 m/s
vf - vi t a

12. One More Acceleration Problem
A car is going 10 m/s when the driver steps on the gas. If the car accelerates at 3 m/s/s, how long does it take the car to reach 40 m/s?
What are we solving for?
Time, t
a = (vf – vi) / t
3 m/s/s = (40 m/s – 10 m/s) / t
3 m/s/s = (30 m/s) / t
t = (30 m/s) / 3 m/s/s
t = 10 s
vf - vi t a

13. Circular Motion
An object traveling in a circle is constantly accelerating.
Constantly changing directions.
Centripetal acceleration
Acc. toward the center of a circular path.

14. Uniform Circular Motion
Uniform circular motion: An object traveling at a constant speed in a circle.
The object below is traveling at a constant speed of 15 m/s and is accelerating. Why?
15 m/s

15. Centripetal Acceleration
An object moving in a circular path is constantly accelerating because its direction is always changing. Direction is a part of velocity.
Ball’s Acceleration
Ball’s Velocity

16. t a Calculations a = (vf - vi) ÷ t t = 3 s a = (32m/s - 10m/s) ÷ (3s)
A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?
GIVEN:
vi = 10 m/s
t = 3 s
vf = 32 m/s
a = ?
WORK:
a = (vf - vi) ÷ t
a = (32m/s - 10m/s) ÷ (3s)
a = 22 m/s ÷ 3 s
a = 7.3 m/s2 a
vf - vi t

17. t a Calculations t = ? t = (vf - vi) ÷ a t = (0m/s-30m/s)÷(-3m/s2)
How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s2?
GIVEN:
t = ?
vi = 30 m/s
vf = 0 m/s
a = -3 m/s2
WORK:
t = (vf - vi) ÷ a
t = (0m/s-30m/s)÷(-3m/s2)
t = -30 m/s ÷ -3m/s2
t = 10 s a
vf - vi t

18. Example video

19. Acceleration Example Problems
A runner whose initial speed is 29 km/h increases her speed to 31 km/h in the final lap to win the race. If the runner takes 0.08 h to complete this increase in her speed, what is her acceleration?

20. Acceleration Example Problems
What is the final speed of a skater who accelerates at a rate of 2.0 m/s2 from rest for 3.5 seconds?

21. Acceleration Example Problems
3) Solid-fuel rocket boosters are used to accelerate space shuttles at a nearly constant total acceleration of 6.25 m/s2. The shuttle’s speed increases from rest to about 750 m/s. How long does it take the shuttle to reach this speed?

22. Graphing Motion
Physical Science

23. Distance-Time Graphs Distance vs Time Graphs
Also known as Position vs Time graphs
Compare distance traveled to time taken

24. Distance-Time Graphs The slope of a distance-time graph = velocity
To find slope:
Pick two points the line passes through.
Find the distance and time for both points.
velocity =
distance 2 – distance 1
time 2 – time 1

25. Key Phrases At Rest Constant Velocity
Ex. Velocity is zero. Object stays at a distance of 3 meters from the start point.
Constant Velocity
Ex. 2 m/s – the object travels 2 meters in every second.
Accelerating – velocity is changing
Ex. 3 m/s/s – every second, the object’s speed increases by 3 m/s.
Change from this point on….

26. Distance-Time Graphs What is the velocity of this object? 250 200
Distance (feet)
150
100 50 2 4 6 8 10 12 14 16 18
Time (minutes)

27. Distance-Time Graphs First, pick two points the line passes through.
First point:
Distance = 50 ft
Time = 0 min
250
200
Distance (feet)
150
100
Second point:
Distance = 100 ft
Time = 10 min 50 2 4 6 8 10 12 14 16 18
Time (minutes)

28. Distance-Time Graphs The object’s speed is 5 ft/min. velocity =
100 ft – 50 ft
10 min – 0 min =
50 ft
10 min
The object’s speed is 5 ft/min.
250
200
Distance (feet)
150
100 50 2 4 6 8 10 12 14 16 18
Time (minutes)

29. Distance-Time Graphs
Here’s the distance-time graph of another object. What is its velocity?
250
200
Distance (feet)
150
100
The line’s slope is zero, so the object is not moving. 50 2 4 6 8 10 12 14 16 18
Time (minutes)

30. Distance-Time Graphs
When is this object moving faster: from 0 to 10 minutes or from 10 to 18 minutes?
250
200
Distance (feet)
150
100
Slope = velocity, so a steeper line means greater velocity. 50 2 4 6 8 10 12 14 16 18
Time (minutes)

31. Interpreting Distance-Time Graphs
Horizontal line = no speed
Line slanted upward = velocity in positive direction
Line slanted downward = velocity in negative direction

32. Velocity-Time Graphs Velocity vs Time Graphs
Compare an object’s velocity to time.
Slope of velocity-time graph = acceleration
Horizontal line = constant velocity
Line slanted upward = positive acceleration
Line slanted downward = negative acceleration

33. Distance-Time and Velocity-Time Graphs2 4 6 8 10 12 14 16 20 30 40 50 60
time (s)
distance (m)
velocity (m/s) 1 3 5
v = 3.75 m/s
v = 1.25 m/s
These two graphs look very different, but they actually describe the same motion.

34. Graphing Motion Specify the time period when the object was...
Speed-Time Graph
Specify the time period when the object was...
slowing down
5 to 10 seconds
speeding up
0 to 3 seconds
moving at a constant speed
3 to 5 seconds
not moving
0 & 10 seconds

35. Where is the object
standing still?
traveling backwards?
traveling at 5m/s?
What is speed at line E?

36. Graphing Acceleration
Acceleration is graphed on a speed / time graph
Accelerated motion will be a curve
Constant acceleration will be a straight line on a speed/time graph
Horizontal lines on a speed / time graph indicates the object is moving at a constant speed..

37. Positive Acceleration
Distance-Time Graph
A positive acceleration indicates that the acceleration points in the positive direction.
Ex: Increasing distance over time or Decreasing time over distance.
“speeding up”

38. Negative Acceleration
A negative acceleration indicates that the acceleration points in the negative direction.
Ex: Decreasing distance over time or Increasing time over distance.
“slowing down”

39. Graphing acceleration video

42. Need more help?