1. Acceleration
Changes in Velocity

2. Acceleration Changing Velocity
There are two major indicators that the velocity of an object has changed over time
Change in spacing of dots
Differences in lengths of velocity vectors
If object speeds up, subsequent velocity vector longer
If object slows down, each vector shorter than previous one

3. Acceleration Acceleration
Acceleration - Rate at which object’s velocity changes
When velocity of object changes at constant rate, has constant acceleration

4. Acceleration
Velocity-Time Graphs

5. Acceleration Average and Instantaneous Acceleration
Average acceleration - Change in velocity during measurable time interval divided by time interval
Instantaneous acceleration - Change in velocity at instant of time
Measured in m/s2

6. Acceleration Average and Instantaneous Acceleration
Instantaneous acceleration found by drawing tangent line on velocity- time graph at point of time in which interested. Slope of line equal to instantaneous acceleration

7. Acceleration Velocity and Acceleration
How would you describe the sprinter’s velocity and acceleration as shown on the graph?
Sprinter’s velocity starts at zero, increases rapidly for first few seconds, then, after reaching about 10.0 m/s, remains almost constant

8. Acceleration Positive and Negative Acceleration
First - positive direction speeding up
Second - positive direction slowing down
Third speeding up negative direction
Fourth slowing down negative direction

9. Acceleration Positive and Negative Acceleration
When speeding up, velocity and acceleration vectors
point in same direction
When slowing down, acceleration and
velocity vectors point in opposite direction
Both direction of velocity and acceleration needed to
determine whether speeding up or slowing down
Positive acceleration when acceleration vector points in
positive direction, and negative when vector points in
negative direction
Sign does not indicate whether object speeding up or slowing down

10. Acceleration Determining Acceleration from v-t Graph
Assume positive direction east
If no slope, acceleration zero
A and E constant velocity
B - positive velocity and constant,
positive acceleration
C negative slope, motion slows down,
and stops (acceleration and velocity opposite)
C and B crossing point shows velocities equal. Does not give runners’ positions

11. Acceleration Determining Acceleration from v-t Graph
D - starts toward west, slows down, for instant zero velocity, then moves east increasing speed. Slope positive. Velocity and acceleration in opposite directions, speed decreases and equals zero at time graph crosses the axis. After that time, velocity and acceleration in same direction and speed increases

12. Acceleration Determining Acceleration from v-t Graph
Average acceleration expressed as slope of velocity-time graph

13. Acceleration Determining Acceleration from v-t Graph
On the basis of the velocity-time graph of a car moving up a hill, determine the average acceleration of the car?

14. Motion with Constant Acceleration
Velocity with Average Acceleration
Average acceleration:
Rewritten as follows:
And rearranged again:

15. Motion with Constant Acceleration
Velocity with Average Acceleration
When acceleration constant; average acceleration, ā, is the same as instantaneous acceleration, a
Equation for final velocity can be rewritten to find time at which object with constant acceleration has given velocity
Also used to calculate initial velocity when both velocity and time given

16. Motion with Constant Acceleration
Position with Constant Acceleration
Graph shows motion not uniform:
Displacements get larger
Slope of constant acceleration gets steeper

17. Motion with Constant Acceleration
Position with Constant Acceleration
Slopes used to create velocity-time graph contains information about displacement
v - height of plotted line above t-axis
Δt - width of shaded rectangle
Area of rectangle is vΔt,
or Δd (displacement)

18. Motion with Constant Acceleration
Position with Constant Acceleration
Graph shows the motion of an airplane. Find the displacement of airplane at Δt = 1.0 s and at Δt = 2.0 s

19. Motion with Constant Acceleration
An Alternative Expression
Often, it is useful to relate position, velocity, and constant acceleration without including time
Pg. 68

20. Motion with Constant Acceleration
An Alternative Expression
Rearrange vf = vi + ātf, to solve for time:
Rewriting di = df + vitf + ātf2 1 2

21. Motion with Constant Acceleration
An Alternative Expression
From the graph as shown, if a car slowing down with a constant acceleration from initial velocity vi to the final velocity vf, write the equation for the total distance (Δd) traveled by the car

22. Motion with Constant Acceleration
An Alternative Expression
On the v-t graph shown on the right, for an object moving with constant acceleration that started with an initial velocity of vi, derive the object’s displacement

23. Free Fall Acceleration due to gravity concept in motion
At the top of its flight, the ball’s velocity is 0 m/s. What would happen if its acceleration were also zero?
The ball’s velocity would remain at 0 m/s
It would simply hover in the air at the top of its flight
Acceleration of an object at the top of its flight can’t be zero. Further, acceleration must be downward

24. Free Fall Acceleration Due to Gravity
Amusement parks use the concept of free fall to design rides that give the riders the sensation of free fall
Rides usually consist of three parts: the ride to the top, momentary suspension, and the plunge downward
When the cars are in free fall, the most massive rider and the least massive rider will have the same acceleration

25. Free Fall What is Free Fall?
Free fall is the motion of the body when air resistance is negligible and the action can be considered due to gravity alone
Gravity = 9.8 m/s2

26. Free Fall Acceleration Due to Gravity
Suppose the free-fall ride at an amusement park starts at rest and is in free fall for 1.5 s. What would be its velocity at the end of 1.5 s?

27. Free Fall Acceleration Due to Gravity
How far does the ride fall? (Hint: Use the equation for displacement when time and constant acceleration are known)