A driver having a definite reaction time is capable of stopping his car over a distance of 30 m on seeing a red traffic signal, when the speed of the car is 72 km/hr andover a distance of 10 m when the speed is 36 km/hr. Find the distance over which he can stop the car if it were running at a speed of 54 km/hr. Assume that his reaction time and the deceleration of the car remains same in all the three cases.

Answer

18.75 m

Explanation

Let `t` second be the reaction time of the driver to be able to put braks and let `a` be the acceleration of the car, when full brakes are applied.
(i) Distance travelled by the car , after the driver has seen the signal and before the driver has just applied the breakes `(i.e. due to reaction time)`
`=velocity`xx`t
`=72(km)/(hr)xxt=20t(m)/(sec)`
Thus the brakes stopped the car within the distance of `(30-20t)`m.
`=(0^2-20^2)/(2xx(20-20t))=(-20^2)/(2xx(30-20t))=-(20)/(30t)`
Similarly
`a=((0-10^2))/(2(10-10t))=(-5)/(1-t)`,`a=((0-15^2))/(2(x-15t))`
when x: distance travelled by car in third case
`(20)/(3-2t)=(5)/(1-t)=(15^2)/(2(x-15t))`
`t=(1)/(2)` sec. `x=18.75`m