Question

A train starts from rest with acceleration 0.2 m/s² on a straight track and then comes to rest after attaining maximum speed on another station due to retardation 0.4 m/s². If total time spent is half an hour, then distance between two stations is (Neglect the length of train)

Answer 1

A-C

\({V_2}^2 - u^2 = 2aS\)

\({V_{max}}^2 -0 = 2 \times (0.2)S\)

\(S_1 = \frac{{V_m}^2}{0.4}\)

\(V = u + at\)

\(\frac{V_{max}}{0.2} = t_1\)

C-B

\({V_1}^2 - u^2 = 2aS\)

\((V_{max})^2 = 2 \times (-0.4) S_2\)

\(S_2 = \frac{(V_{max})^2}{0.8}\)

\(V = u + at\)

\(0 = V_{max} - 0.4\)

\(t_2 = \frac{V_{max}}{0.4}\)

\(t_1 + t_2 = 30 \times 60\)

\(\frac{V_{max}}{0.2} + \frac{V_{max}}{0.4} = 1800\)

\(\frac{2V_{max}}{0.4} + \frac{V_{max}}{0.4} = 1800\)

\(3V_{max} = 1800 \times \frac 4{10}\)

\(V_{max} = 240 \,m/s\)