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 data.

1. The acceleration of a boat is $3.0m{s}^{-2}$.
2. The initial speed is zero.
3. The total time of acceleration is $8.0s$.

Step 2: Concept and formula to be used.

According to the second equation of motion, $s=ut+\frac{1}{2}a{t}^2$ where, $s$ is the total distance covered, $u$ is the initial speed, $a$ is the acceleration and $t$ time of the journey.

Step 3: Find the total distance covered by the boat.

Since, the initial speed of the boat is zero, the time of journey is $8.0s$ and the acceleration is $3.0m{s}^{-2}$.

So, the total distance $s$ covered is given by:

$$\begin{gathered} s=\frac{1}{2}\left(3\right)\left(8\right)\left(8\right) \\ \Rightarrow s=96m. \end{gathered}$$

Therefore, the total distance covered by the boar during the given time is $96m$.