Homework SourseThe following trajectory data was obtained during an experim
The following trajectory data was obtained during an experiment on particle motion
Time (s)
Velocity (m/s)
0
0
1
1
2
3
3
4
4
5
5
4
6
4
7
3
8
2
9
1
10
1
Using both the analytical and numerical methods:
a. Determine the distance traveled by the object between times t=1 and t=5 seconds.
b. Determine the acceleration at initial time (t=0)
c. Determine dv/dt at t=7 seconds.
| Time (s) | Velocity (m/s) |
| 0 | 0 |
| 1 | 1 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |
| 5 | 4 |
| 6 | 4 |
| 7 | 3 |
| 8 | 2 |
| 9 | 1 |
| 10 | 1 |
Solution
a) distance traveled by the object between times t=1 and t=5 seconds = 1 + 3 + 4 + 5 + 4 = 17 m
b) acceleration at initial time (t=0) = no change in the rate of velocity = 0 acceleration
c) u = ds/dt = 4, at t=6 and v = ds/dt = 3, at t=7 seconds
then a = dv/dt = (v - u)/t = (3 - 4)/(7 - 6) = -1 m2/s
