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?

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Solution

## Step 1: Given data. The acceleration of a boat is $3.0m{s}^{-2}$.The initial speed is zero.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:$s=\frac{1}{2}\left(3\right)\left(8\right)\left(8\right)\phantom{\rule{0ex}{0ex}}⇒s=96m.$Therefore, the total distance covered by the boar during the given time is $96m$.

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