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

Given: A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of $3.0\ ms^{-1}$ for $8.0\ s$. 

To do: To find the distance traveled by boat during this time.

Solution:

The motorboat starts from rest. So its initial velocity u = 0 m/s

given $a = 3\ m/s^2$

time, $t = 8\ seconds$

Distance traveled in 8 seconds

$S = ut + \frac{1}{2}\times at^2$

$=0\times 8 + \frac{1}{2}\times 3\times 8^2$

$=0 + \frac{1}{2}\times 3\times  8^2$

$=\frac{1}{2} \times 3 \times 64$

$=96 m$