Question

A train of length 200 m switches on its headlights when it starts moving with acceleration 0.5 m/sec². Sometime later , its tail light is switched on. An observer on the ground notices that two events occur at the same place. The time interval between the two events is K x 10√2. Then find the value of K.

Answer 1

Dear student,

The train covers its length in given time interval.
$$\begin{gathered} s=ut+\frac{1}{2}a{t}^2 \\ \Rightarrow 200=0+\frac{1}{2}\times 0.5t^2 \\ \Rightarrow t=\sqrt{200\times 4}=20\sqrt{2} \\ \Rightarrow K10\sqrt{2}=20\sqrt{2} \\ \Rightarrow K=2 \end{gathered}$$
Regards.