# Stopping Distance

## Stopping Distance

When an object is moving with a certain velocity then suddenly brakes are applied, and then object stops completely after covering a certain distance. This is called as stopping distance. It is the distance travelled between the time when an object deiced to stop a moving vehicle and the time when the vehicle stops completely. It depends on the factors including road surface and reflexes of the car’s driver and the stopping distance is denoted by d.

$$Stopping\text{ }Distance\left( d \right)=\frac{{{V}^{2}}}{2\mu g}$$ (Or) $$Stopping\text{ }Distance\left( d \right)=k{{V}^{2}}$$

Where,

V = Velocity $$\left( m/\sec \right)$$

$$\mu =$$ Co-efficient of friction

$$g=$$Acceleration due to gravity$$\left( m/{{\sec }^{2}} \right)$$

$$k=$$ Constant of Proportionality

How to calculate the Stopping Distance:

Problem: A vehicle moves with a velocity $$20m/\sec$$ and applies a brake. Calculate the stopping distance if constant of proportionality is 0.5.

Solution:

Given,

Velocity$$\left( V \right)=20m/\sec$$

Constant of proportionality$$\left( k \right)=0.5$$

Stopping distance (d) =?

We know that:

Stopping distance (d)$$=k{{V}^{2}}$$

$$\Rightarrow Stopping\text{ }distance(d)=0.5\times {{\left( 20m/\sec \right)}^{2}}=200m.$$