Question

William was swimming at a speed of 3 m/s when he started to slow down. He slowed to a stop in 2 seconds. What is his acceleration?

Answer 1

`-1.5\;\rm m \cdot s^(-2)` on average.

Step-by-step explanation:

The acceleration of an object is the rate of change in its velocity. The average acceleration of an object is equal to the change in velocity over the time required for that change to take place.

For the William in this question:

• The initial speed of William is
  `3\; \rm m \cdot s^(-1)`.
• Because William came to a complete stop after
  `2\; \rm s`, his speed at that time would be
  `0\; \rm m \cdot s^(-1)`.

Had William not came to a complete stop, it would be necessary to consider whether there is a change to his orientation. However, because in this question William came to a stop, the change in his velocity would be:

`\begin{aligned} &\text{Change in velocity} \\&= \text{Final velocity} - \text{Initial velocity}\\ &= 0\; \rm m \cdot s^(-1) - 3\; \rm m \cdot s^(-1) = -3\; \rm m \cdot s^(-1)\end{aligned}`.

That change in velocity happened over
`2\; \rm s`. Therefore, the average acceleration would be:

`\begin{aligned}&\text{Average Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}} = (-3\; \rm m \cdot s^(-1))/(2\; \rm s) \approx -1.5\; \rm m \cdot s^(-1)\end{aligned}`.