Kinetic Energy and Stopping Distance

Kinetic energy

All moving objects have kinetic energy. The kinetic energy Ek of an object with a mass of 'm' and a velocity of 'v' can be calculated as follows.

$E_{ k }=\frac { 1 }{ 2 } m{ v }^{ 2 }$

In other words, the kinetic energy of an object is proportional to the mass of the object and proportional to the square of the speed.

Stopping distance

When you try to stop the car, the car does not stop immediately. "Stopping distance" refers to the distance the vehicle travels while the brake is operating.
By definition of work (work = force x distance), the kinetic energy of the car is equal to the braking force multiplied by the stopping distance.

$Kinetic energy =\frac { 1 }{ 2 } m{ v }^{ 2 }=braking force \times stopping distance$

Assuming that the braking force is constant, the stopping distance is proportional to the square of the speed of the car.
In other words, when the speed is doubled, tripled or quadrupled, the stopping distance increases by 4, 9, or 16 times. That's why it's dangerous when accidents happen on the highway.