# Stopping Distance Formula

When the body is moving with a certain velocity and suddenly brakes are applied. You would have noticed that the body stops completely after covering a certain distance. This is called stopping distance.

The stopping distance is the distance traveled between the time when the body decides to stop a moving vehicle and the time when the vehicle stops completely. The stopping distance depends on factors including road surface, and reflexes of the car’s driver and it is denoted by d.

Stopping Distance formula is given by,

$d\,&space;=\,&space;\frac{V^{2}}{2\mu&space;g}$

Where,

v = velocity,

μ = friction coefficient,

g = acceleration due to gravity.

The stopping distance formula is also given by,

$d\,&space;=\,&space;kv^{2}$

Where,

k = a constant of proportionality

v = speed.

Example 1

A car is moving with a velocity of 40 m/s and suddenly applies brakes. Determine the constant of proportionality if the body covers a distance of 10 m before coming to rest.

Solution:

Given:

Velocity v = 40 m/s,

Stopping distance d = 10 m,

The constant of proportionality is given by the formula,

k = d / v2

= 10 / 1600

= 0.00625.

Example 2

A bike moves with a velocity of 15 m/s and applies a brake. Calculate its stopping distance if the constant of proportionality is 0.9.

Solution:

Given:

Velocity v = 15 m/s,

Constant of proportionality k = 0.9,

the stopping distance is given by

d = k v2

= 0.9 × 225

= 202.5 m