Question

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of $3.0m{s}^{-2}$ for $8.0s$. How far does the boat travel during this time?

Answer 1

Step 1: Given

The initial velocity of a motorboat, $u=0$

Acceleration of motorboat, $a=3.0m{s}^{-2}$

Time under consideration or time is taken $t=8.0s$

Step 2: Applying the second motion equation for determining the value of distance

As we have, from the second motion equation, we have, $s=ut+\frac{1}{2}a{t}^2$

Here $s$is displacement and $u$is initial velocity and $t$ is time and $a$ is acceleration.

So, the value of distance will be

$$\begin{gathered} s=(0\times 8)+\frac{1}{2}\times 3\times 8^2 \\ \Rightarrow s=0+\frac{1}{2}\times 3\times 64 \\ \Rightarrow s=96m \end{gathered}$$

Therefore, the distance traveled by motorboat $=96m$.