# If you double the speed of a vehicle how much does the force in a crash increase by?

##### 2 Answers

The force will be between twice as great and four times as great, depending on some assumptions we make.

#### Explanation:

The force exerted by a vehicle in a crash will arise from its impulse, a measure of the change in its momentum. Usually the momentum starts high before the collision and ends up at zero after the collision.

The impulse is given by

The impulse will be the change in momentum, from

If we double the velocity, we go from v to 2v, so the expression changes to:

This looks as though the force just doubles, but note that the time taken for the collision is likely to be shorter if the vehicle's velocity is higher. This is not a simple 1:1 relationship because it has to do with how the vehicle crumples, but if it did the time would be half as long:

If that were the case, the force would be 4 times as great.

Quadruple

#### Explanation:

We know that

We also know that

Solve for

Speed is simply the absolute value of

Square the

We can use

So doubling the speed will quadruple the force.