Question

A train stopping at two stations $2 \,km$ apart on a straight line takes $4$ minutes for the journey. Assuming that its motion is first uniformly accelerated and then uniformly retarded. If $\frac{1}{x} + \frac{1}{y} = n$, where $;x'$ and $'y'$ are the magnitudes of the acceleration and retardation respectively. Find the value of $n$

• A. 2
• B. $\frac{1}{2}$
• C. 4
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

Total time taken $= 4 \,\min$
(i) $\frac{v_0}{x} + \frac{v_0}{y} = 4\,\min$
(ii) Total distance travelled $= 2 \,km$
$\Rightarrow $ Area under $v - t$ graph $= 2 \,km$
$\frac{1}{2} \times \frac{v_0}{x} \times v_0 + \frac{1}{2} \times \frac{v_0}{y} \times v_0 = 2\,km$
From (i) and (ii), $\frac{1}{x} + \frac{1}{y} = 4$