# Stopping Distance Formula

## 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 the stopping distance.

The stopping distance is the distance travelled 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 carâ€™s driver and it is denoted by d.

Stopping Distance formula is given by,

$d=\frac{v^{2}}{2\mu g}$

Where,

d = stopping distance (m)

v = velocity (m/s)

Î¼ = friction coefficient

g = acceleration due to gravity (9.8Â $m/s^{2}$)

The stopping distance formula is also given by,

$d=kv^{2}$

Where,

k = a constant of proportionality

v = velocity

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,

$k=d/v^{2}$

Â Â = 10 / 1600

Â Â = 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

$d=kv^{2}$

Â Â = 0.9 Ã— 225

Â  d = 202.5 m