Question

A train of length L accelerates uniformly from rest. If the front of the train passes a railway worker a distance x down the track at a speed of v, what will be the speed v_L of the last car as it passes the worker? Express your answer in terms of the given symbols.

Answer 1

Here,

let the acceleration of the train is a

when it travels a distance x , it's velocity becomes v

Using third equation of motion

v^2 - 0^2 = 2 * a * x

a = v^2/(2x)

NOw, for total distance (L + x)

vL^2 - 0^2 = 2 * a * (x + L)

vL^2 = 2 * v^2 * (x + L)/(2x)

vL = v * sqrt((x+L)/x)

the final velocity of the last car is v * sqrt((x+L)/x)