Kinetic energy

Kinetic energy (Ek or KE) is the energy of motion. Any object that has mass and is moving has kinetic energy because it is moving. When you catch a ball, your hand applies a force over some distance (your hand recoils a bit) to stop the ball. That force multiplied by the distance represents the transfer of the ball’s kinetic energy to your hand by doing work on your hand. Now think about catching balls of different masses and speeds. You can probably guess that a massive or a fast-moving ball has more kinetic energy—it is harder to stop!—than a lighter, slower ball. Read the text aloud
(9.2) E k = 1 2 m v 2
Ek  = kinetic energy (J)
m  = mass (kg)
v  = speed (m/s)
Kinetic energy
Kinetic energy is calculated using equation (9.2) above. The kinetic energy of a moving object is proportional to mass. If you double the mass, you double the kinetic energy. For example, a 2 kg ball moving at a speed of 1 m/s has 1 J of kinetic energy according to the equation. A 4 kg ball moving at the same speed has 2 J of kinetic energy, or twice as much. This is a linear relationship. Read the text aloud Kinetic energy is proportional to mass and proportional to speed squared
According to equation (9.2) kinetic energy depends on the square of the speed of a moving object. Consider a 2 kg ball traveling at 1 m/s with 1 J of kinetic energy. The same ball moving at 3 m/s has 9 J of kinetic energy. If you multiply the speed by 3, then the kinetic energy is multiplied by a factor of 32 = 9. This is an example of a nonlinear relationship. Read the text aloud Show Nonlinear relationships
The fact that kinetic energy increases with the square of the speed has implications for the stopping distance of a car. As a car brakes, work is done to transform the car’s kinetic energy into thermal energy. Work is force multiplied by distance. Assuming that the braking and road conditions result in a relatively constant stopping force, then the distance it takes the car to stop is proportional to the initial kinetic energy. At 30 mph a car can stop in about 15 m. When the speed is doubled to 60 mph (and the kinetic energy increases by a factor of 4) it takes four times as much distance to stop. Read the text aloud
Braking distance increases as the square of the car's speed
A motorcycle has 10 J of kinetic energy. If its velocity is doubled, how much kinetic energy does it now possess?
  1. 15 J
  2. 20 J
  3. 35 J
  4. 40 J

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