# Vehicle Stopping Distance Calculation Equations and Example

Imagine you are driving, you suddenly see a obstacle in the middle of the road. Now, before you actually press the brake pedal, you, as a human being, will take some time for thinking or analyzing the situation. This time is called thinking time and the distance covered during this time is called thinking distance.

Actual breaking occurred after thinking time is over. The distance covered between the pressing of the brake pedal and stopping the car is called breaking distance.

So, technically,

Stopping distance = Thinking distance + Breaking distance ………………..eq.1

Now, the first term of the right hand side of the above stopping distance equation (eq.1) depends upon the state of mind of the driver and obviously varies from person to person.

However, as a rule of thumb,

Thinking distance = 3.33 x u  …………………………….eq.2

Where,

u – Velocity at which the vehicle is moving at the instant when the brake is applied

Breaking Distance Calculation

As soon as you apply brake, the sliding friction between the tire and road comes into the picture.

In this condition,

F = μs x Wf  + μs x Wr =  μs x (Wf + Wr )= μs x W = μs x m x g …………….eq.3

Where,

μs – Sliding coefficient of friction between tire and road

Wf – Vehicle weight on front wheel

Wr – Vehicle weight on rear wheel

W – Total vehicle weight

m – mass of the vehicle

g – gravitational acceleration

Also, from newton’s law,

F = m x a  ……………………………………………….eq.4

Where,

a – Acceleration / deceleration of the vehicle

From the eq.3 and eq.4,

F = m x a = μs x m x g

⇒ a = μs x g  …………………………………………..eq.5

Finally, we will require the following equation,

u2 = 2 x a x S …………………………………………….eq.6

Where,

S – Braking distance

u – Velocity at which the vehicle is moving at the instant when the brake is applied

a – Acceleration / deceleration of the vehicle

So, you can see from the eq.6, you can get the braking distance value. Combining this with the thinking distance value (eq.1 and eq.2) will get you the stopping distance. How? See the example below:

Example: Calculate the stopping distance of a car which is moving at a velocity of 60 KMPH. The car is moving on a dry asphalt road.

Solution:

Given data:

u = 60 KMPH = 16.67 Meter / hr

From eq.2,

Thinking distance = 3.33 x u = 3.33 x 16.67 = 55.5 Mtr.

From eq.5,

a = μs x g = 0.5 x 9.81 = 4.905 Mtr/sec2

From eq.6,

u2 = 2 x a x S

⇒16.672 = 2 x 4.905 x S

⇒ S = 28.32 Mtr.

From eq.1,

Stopping distance = Thinking distance + Breaking distance = 55.5 + 28.32 = 83.82 Mtr.

The above example shows how to calculate stopping distance of a car (or truck or any vehicle) using stopping distance formulas.