Question

Two cars are moving on a straight road with one car200 m away from the other moving at the same speed . at acertain moment brakes are applied to the rear car which decelerates uniformly traveling 40m be before coming to rest find the distance between the cars at the moment when the rear car comes to rest.

Answer 1

Dear student,

Let A and B be the positions of two cars such that AB = 200m
C be the position of rear car after coming to rest and
D be the position of first car
CD be the distance between two cars after the rear car comes to rest.

A-----C---------B---------------D

CB = 180m
AC = 20m
AB = 200m

CD=? From figure, CD=CB+BD=180+BD
CD=180+ut (S=velocity x time) .......(1)
Applying S=ut+1/2at² for AC, we get 20=ut+1/2at² ......(2) (DE=(2x)body is retarding) and
v=u+at
=>0=u−at
=>u=at
=>a=u/t
Substituting value of a in (2)we get,
20=ut−1/2×(u/t)×t²
=>20=ut−1/2ut
=>ut=40 .......... (3)
Substituting (3) in (1) we get,
CD=180+BD=180+40=220m.
Regards,