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

a) Since the Force that stops the car is constant and the mass of car is too then the ratio of force to mass will also be constant,i.e, the acceleration will be constant let this value be 'a' m/s2

let the distance travelled in first case(50 km/hr) be s1 and in second case (100 km/hr) be s2

from equation of motion (since final velocity is zero) v2-u2=-2as {a is negative because it is deceleration}

we can say that u2 is propotional to distance travelled s

s2/s1 = (u2/u1)2  

s2/s1=(100/50)2=22

s2/s1=4

b) let time in first case be t1 and in second case be t2

since we know that, v=u-at

thus t is proportional to u

t2/t1 = u2/u1

t2/t1=100/50=2

t2

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