PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A cart travels back and forth on a straight track. A motion sensor records the following average velocities at equally spaced times and calculates an estimate of the cart’s acceleration at those times. The data are shown in the table.
```
t (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6
------------------------------------
v (m/s) | 0.0 | 1.8 | 3.0 | 2.4 | 0.6 | –1.2 | –3.0
a (m/s^2) | — | 1.9 | 1.2 | –0.6 | –1.8 | –2.1 | –1.8
```
(The dash at t=0 indicates that acceleration is not estimated at the initial instant.)
(a) Using the data, estimate all open intervals on 0<t<6 seconds during which the cart’s speed was increasing and all intervals during which its speed was decreasing. Clearly indicate how you used the table to reach your answer.
(b) Explain why your answer in part (a) might change if more frequent measurements were taken. Describe one specific way in which finer time intervals could affect your identification of speed increases and decreases.