Consider the motion of an object along a
straight path as shown in the figure.
1
0 1 2 3 4 5 6 7 8 9
b
b
b
b
b b
b b
time (s)
velocity (m/s)
Find the average acceleration during the
time interval 0 s to 3 s.
Answer in units of m/s
2
005 (part 2 of 6) 10.0 points
Find the average acceleration during the time
interval 3 s to 6 s.
Answer in units of m/s
2
006 (part 3 of 6) 10.0 points
Find the average acceleration during the time
interval 0 s to 9 s.
Answer in units of m/s
2
007 (part 4 of 6) 10.0 points
Find the instantaneous acceleration at 2 s.
Answer in units of m/s
2
008 (part 5 of 6) 10.0 points
Find the instantaneous acceleration at 4 s.
Answer in units of m/s
2
009 (part 6 of 6) 10.0 points
Find the instantaneous acceleration at 7 s.
Answer in units of m/s
2
To find the average acceleration during a time interval, you need to know the change in velocity and the time elapsed. Average acceleration is calculated using the formula:
average acceleration = (change in velocity) / (time interval)
For the given motion, we can determine the average acceleration for each time interval as follows:
1. Time interval 0s to 3s:
- Find the change in velocity by subtracting the initial velocity from the final velocity.
- In this case, the initial velocity is 0 m/s and the final velocity is 3 m/s.
- The change in velocity = 3 m/s – 0 m/s = 3 m/s.
- The time interval is 3s – 0s = 3s.
- Average acceleration = (change in velocity) / (time interval) = 3 m/s / 3 s = 1 m/s^2.
2. Time interval 3s to 6s:
- Find the change in velocity by subtracting the initial velocity from the final velocity.
- In this case, the initial velocity is 3 m/s and the final velocity is 6 m/s.
- The change in velocity = 6 m/s – 3 m/s = 3 m/s.
- The time interval is 6s – 3s = 3s.
- Average acceleration = (change in velocity) / (time interval) = 3 m/s / 3 s = 1 m/s^2.
3. Time interval 0s to 9s:
- Find the change in velocity by subtracting the initial velocity from the final velocity.
- In this case, the initial velocity is 0 m/s and the final velocity is 9 m/s.
- The change in velocity = 9 m/s – 0 m/s = 9 m/s.
- The time interval is 9s – 0s = 9s.
- Average acceleration = (change in velocity) / (time interval) = 9 m/s / 9 s = 1 m/s^2.
4. Instantaneous acceleration at 2s:
- Instantaneous acceleration refers to the acceleration at an exact moment in time.
- To get the instantaneous acceleration at 2s, we need to know the velocity at exactly 2s.
- From the figure, it is not clear what the velocity is at 2s. You need to provide more information, such as the position of the object at 2s or any additional data.
5. Instantaneous acceleration at 4s:
- Similar to the previous question, we need the velocity at exactly 4s to calculate the instantaneous acceleration.
- Without that information, we cannot determine the instantaneous acceleration at 4s.
6. Instantaneous acceleration at 7s:
- Again, we need the velocity at exactly 7s to calculate the instantaneous acceleration.
- Without that information, we cannot determine the instantaneous acceleration at 7s.