**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 carâ€™s driver and it is denoted by d.

Stopping Distance formula is given by,

Where,

v = velocity,

Î¼ = friction coefficient,

g = acceleration due to gravity.

The stopping distance formula is also given by,

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,

Â Â Â Â Stopping distance d = 10 m,

The constant of proportionality is given by the formula,

k = d / v2

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,

Â Â Â Â Constant of proportionality k = 0.9,

the stopping distance is given by

d = k v2

Â Â = 0.9 Ã— 225

Â Â = 202.5 m