Kinetic Energy Physics Example 4

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Example 4

easy
A 1200 kg1200 \text{ kg} car doubles its speed from 15 m/s15 \text{ m/s} to 30 m/s30 \text{ m/s}. By what factor does its kinetic energy increase?

Solution

  1. 1
    Initial KE: KE1=12(1200)(15)2=12(1200)(225)=135,000 JKE_1 = \frac{1}{2}(1200)(15)^2 = \frac{1}{2}(1200)(225) = 135{,}000 \text{ J}.
  2. 2
    Final KE: KE2=12(1200)(30)2=12(1200)(900)=540,000 JKE_2 = \frac{1}{2}(1200)(30)^2 = \frac{1}{2}(1200)(900) = 540{,}000 \text{ J}.
  3. 3
    Factor: 540,000135,000=4\frac{540{,}000}{135{,}000} = 4.

Answer

Kinetic energy increases by a factor of 44
Because kinetic energy depends on the square of the speed, doubling the speed quadruples the kinetic energy. This is why high-speed collisions are so much more dangerous.

About Kinetic Energy

The energy an object possesses by virtue of its motion, equal to one-half times its mass times the square of its velocity.

Learn more about Kinetic Energy →

More Kinetic Energy Examples

Example 1 easy

What is the kinetic energy of a [formula] ball moving at [formula]?

Example 2 medium

A car doubles its speed from [formula] to [formula]. By what factor does its kinetic energy change?

Example 3 medium

A [formula] ball has [formula] of kinetic energy. What is its speed?

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