A motorboat is moving in a straight line on a lake with an initial...

Using the third equation of motion, $v^2 = u^2 + 2as$.

For the first part of the motion, the initial velocity is $v$, final velocity is $\dfrac{v}{2}$, and distance $s = 60\text{ m}$.

\left(\dfrac{v}{2}\right)^2 = v^2 + 2a(60)$<br><br>$\dfrac{v^2}{4} - v^2 = 120a$<br><br>$-\dfrac{3v^2}{4} = 120a \Rightarrow a = -\dfrac{v^2}{160}$<br><br>Let the total distance covered before coming to rest be$S$. The final velocity is$0$.<br><br>$0 = v^2 + 2aS$<br><br>$0 = v^2 + 2\left(-\dfrac{v^2}{160}\right)S$<br><br>$\dfrac{v^2}{80}S = v^2 \Rightarrow S = 80\text{ m}$<br><br>Answer:$80\text{ m}