Question

A car starting from rest accelerates at the rate $f$ through a distance $S$, then continues at constant speed for time $t$ and then decelerates at the rate $f/2$ to come to rest. If the total distance traversed is $5S$, then

• A. $S=ft$
• B. $S=1/6f{t}^2$
• C. $S=1/2f{t}^2$
• D. $S=1/4f{t}^2$

Answer 1

The correct option is C $S=1/2f{t}^2$

$s_1+s_2+s_3=5s$
$\Rightarrow s+vt+\frac{v^2}{f}=5s$
$\Rightarrow 4s=vt+\frac{v^2}{f}=\sqrt{2fs}\times t+\frac{2fs}{f}$
$\Rightarrow 2s=t\sqrt{2fs}\Rightarrow s=\frac{1}{2}f{t}^2$.