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

 A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 ms-1 for 8.0s. How far does the boat travel during this time?

Solution:

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

given a = 3 m/s²

time, t = 8 seconds

Distance travelled 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