A car traveling 50 km/h can be brought to a stop in a particular distance under

Question

A car traveling 50 km/h can be brought to a stop in a particular distance under controlled braking conditions. For this problem, ignore the reaction time of the driver and find the stopping distance and stopping time after the brakes are applied.
(a) Assuming the force used to bring the car to rest is the same, how much distance is required to bring the car to a stop if the car is traveling 100 km/h, twice as fast as it was originally? The distance in this case is larger than the original distance by a factor of:

(b) How do the stopping times compare? The stopping time in the second case is larger than the original stopping time by a factor of:

Explanation / Answer

since force is constant accelaration is also constant a(say) we have v^2 - u^2 = 2*a*s where u=intial velocity;v=final velocity;a=accelaration;s=distance in the intial case when u=50 we have 0-50^2=2*a*si si=-50^2/(2*a) ------- eq1 (a) now, when u=100 we have 0-100^2=2*a*sf sf=-100^2/(2*a) --------eq2 now divide eq2 by eq1 that gives sf/si = 100^2/50^2 =4 so,the distance in this case is larger than the original distance by a factor of 4 (b) let ti be the initial original stopping time then from v=u+a*t we have 0=50+a*ti ti=-50/a -----------eq3 now when v=100 we have 0=100+a*tf tf=-100/a ---------- eq4 now divide eq4 by eq3 we get tf/ti = 100/50 =2 so,the stopping time in the second case is larger than the original stopping time by a factor of 2.

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