Applications: braking and road safety

Why speed is so dangerous

As E_c = 1/2 * m * v^2, kinetic energy increases with the square of the speed. Doubling a vehicle’s speed therefore quadruples its kinetic energy, and the braking distance required to dissipate it (assuming constant braking force) is also approximately quadrupled.

Braking distance

According to the kinetic energy theorem, if a (constant) braking force F acts over a distance d to bring a vehicle to a halt:

0 – 1/2 * m * v^2 = -F * d, so d = (m * v^2) / (2 * F)

It is clear that d is proportional to v^2.

Example

At 50 km/h, a car travels a certain braking distance. At 100 km/h (twice the speed), with the same braking force, the braking distance is approximately four times greater, because (2v)^2 = 4 * v^2.

Other applications

• Airbags and crumple zones absorb kinetic energy during a collision to protect the occupants.
• In free fall, the kinetic energy gained comes from the conversion of gravitational potential energy.
• Rollercoasters constantly convert potential energy into kinetic energy and vice versa.

A common misconception

Many people think that doubling your speed requires twice the distance to stop. In reality, it is about four times as much, because of the square of the speed. This is one of the reasons why speed limits are so strict.