For a train engine moving with speed of 20   ms – 1 , the driver must apply brakes at a distance of 500   m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed x   ms - 1 . The value of x is ______. (Assuming same retardation is produced by brakes)

Step-by-step solution

Given that, the initial velocity u = 20   m / s , the distance of the station S 1 = 500   m , and the final velocity v = 0 . The relation between the distance travelled S by the train with its initial velocity u and its final velocity v is given by v 2 =   u 2 - 2 a S . . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) where, a indicates the retardation of the train. Substitute the values corresponding to the initial condition into equation (1) and solve to calculate the retardation of the train. 0