Question

A train stopping at two stations $2km$ 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 $;x^{\prime }$ and ${}^{\prime }{y}^{\prime }$ 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 $=2km$

$\Rightarrow$ Area under $v-t$ graph $=2km$

$\frac{1}{2}\times \frac{v_0}{x}\times v_0+\frac{1}{2}\times \frac{v_0}{y}\times v_0=2km$

From (i) and (ii), $\frac{1}{x}+\frac{1}{y}=4$