As speed increases, what happens to kinetic energy?
Speed is equal to distance divided by time. Velocity is speed in a particular direction. For the purposes of your question, we can think of speed and velocity as being the same thing.
Kinetic energy (KE) is the energy of motion. Any object that is in motion has kinetic energy. Kinetic energy is described by the following equation, where m = mass of the object (kg) and v = velocity:
KE = 1/2 x m x `~v^2`
Therefore, the kinetic energy of an object is proportional to the square of its velocity (speed). In other words,
- If there is a twofold increase in speed, the kinetic energy will increase by a factor of four.
- If there is a threefold increase in speed, the kinetic energy will increase by a factor of nine.
- If there is a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen.
Kinetic energy is related to an object's momentum. For a rigid body traveling in a linear path, kinetic energy increases with the square of velocity. So if the velocity doubles, the kinetic energy quadruples! This relationship partially explains the interesting observation that for a collision of a vehicle going 10 miles per hour with a stationary pedestrian, about 7 people out of 10 will survive the accident; for the same collision with the vehicle going twice as fast, only about 1 person will survive the accident. The vehicle going twice the speed has double the kinetic energy to transmit to the pedestrian!