Answer to Question #309320 in Mechanics | Relativity for kin

Question

A KTM commuter train travels between two stations, A and B. The train starts from rest from station A and accelerates at a constant rate for 0.5 km until it reaches a speed of 30 m/s. It then travels at this constant speed for T s before decelerating at a constant rate of 1.5 m/s² and coming to rest at station B. Figure 1 shows the velocity-time graph of the train’s journey between the two stations. Determine the value of T if the distance between the two stations 6 km. Calculate also the total time taken for the whole journey.

Answer 1

$d=l-l_1-l_2=l-\frac{v^2}{2a_1}-\frac{v^2}{2a_2}=4~km,$

$T=\frac d v=133^s,$

$t=T+\sqrt{\frac{4(l-q)}{a_1+a_2}}=283^s.$