Question

The last car is uncoupled from the moving train. The train continues at the same speed. Considering that the car is slowing with constant deceleration, find how many times the distance travelled by the car to its stop is less than distance travelled by train till that moment.​

Answer 1

let the common speed be V

after detaching speed of train=V

but initial speed of car becomes=V

u=V

final speed of car

v=0

let the deceleration be

a=-a

time taken to stop be t

then

distance travelled by train in t sec

=Vt

v²-u²=2as

0-V²=2*(-a)s

s=V²/2a

therefore

distance travelled by train/distance travelled by car=V²t/V²/2a

=2at

Hope this helps.