Physics

Problem

A car moving on a straight test track has the following velocities at different instants: • at

t = 2.0\,\text{s}

v = 10\,\text{m s}^{-1}

• at

t = 7.0\,\text{s}

v = 34\,\text{m s}^{-1}

• at

t = 14.0\,\text{s}

v = 22\,\text{m s}^{-1}

a. (i) Calculate the average acceleration during the interval

2.0\,\text{s}

7.0\,\text{s}

. b. (ii) Calculate the average acceleration during the interval

7.0\,\text{s}

14.0\,\text{s}

. c. (iii) Calculate the average acceleration for the overall interval

2.0\,\text{s}

14.0\,\text{s}

. State whether the acceleration is positive or negative in each case.

Intuitive explanation

This problem tests your understanding of acceleration as the rate of change of velocity. The key insight is that acceleration isn't constant over the whole interval—you need to calculate it separately for each time segment by finding $\Delta v / \Delta t$ . Notice the car speeds up, then slows down, which tells you the acceleration changes sign partway through.

Intuitive explanation

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