Problems on stopping distance

A vehicle is moving on a plane road with a velocity of 100 km/hr. The proportionality constant k is given 1/2 for braking system . What will be the stopping distance of the vehicle?

Option:

a. 380.8 m
b. 385.8 m
c. 300.8 m
d. 400.8 m

Correct Answer : b. 385.8 m

Explanation:

Suppose a vehicle is travelling with a certain velocity and suddenly brake is applied. The distance covered by the vehicle after application of brakes till the vehicle stops is called as stopping distance.

Stopping distance (d) depends upon velocity of the vehicle (v), coefficient of friction between road surface and vehicle tyres (μ) and acceleration due to gravity (g).

The stopping distance is calculated by the formula given,

d = (v²)/2μg

d = kv²

where, k = 1/2μg
constant of proportionality
From the example given,

v = 100 km/hr = (100 * 1000) / 3600 = 27.7778 m/s

Therefore, Stopping distance

d = (1/2) (27.7778²)
d = 385.80 m