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 $15S$, then

• A. $S=\frac{1}{2}f{t}^2$
• B. $S=\frac{1}{4}f{t}^2$
• C. $S=\frac{1}{72}f{t}^2$
• D. $S=\frac{1}{6}f{t}^2$

Answer 1

The correct option is C $S=\frac{1}{72}f{t}^2$


$S\text{'}\text{'}=\frac{v^2}{2\left(f/2\right)}butS=\frac{v^2}{2f}\therefore S\text{'}\text{'}=2SandS\text{'}=12Sand12S=vt......\left(1\right)and{v}^2=2fS......\left(2\right)from\left(1\right)and\left(2\right)144S^2=\left(2fS\right).t^2\therefore S={\frac{ft}{72}}^2$