Question 117 of 308

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 $15 \mathrm{~S}$, then

A$S=f t$B$\mathrm{S}=1 / 6 \mathrm{ft}^2$C$\mathrm{S}=1 / 2 \mathrm{ft}^2$DNone of these

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Answer: (D) None of these

$$\begin{aligned} & \mathrm{S}=\frac{\mathrm{ft}_1^2}{2} \\ & \mathrm{v}_0=\sqrt{2 \mathrm{Sf}} \end{aligned}$$
During retardation
$$S_2=2 S$$
During constant velocity
$$\begin{aligned} & 15 \mathrm{~S}-3 \mathrm{~S}=12 \mathrm{~S}=\mathrm{v}_0 \mathrm{t} \\ & \Rightarrow \mathrm{S}=\frac{\mathrm{ft}^2}{72} \end{aligned}$$