What Is Kinetic Energy?
When you have objects in motion, you have kinetic energy. When, for example, you slide an object on a frictionless surface, the work you do goes into the object’s kinetic energy:
W = KE_{f} – KE_{i}
If you have an object with mass m moving at speed v, its kinetic energy is
That’s the energy of motion.
Sample question

Say that you push a spaceship, mass 1,000.0 kg, by applying a force of 1.00 x 10^{4} N for 1.00 m. How fast does the spaceship end up traveling?
The correct answer is 4.47 m/s.

Find the total work done:
(1.00 x 10^{4} N)(1.00 m) = 1.00 x 10^{4} J

The work done on the spaceship goes into its kinetic energy, and its initial kinetic energy is 0, so its final kinetic energy is 1.0 x 10^{4} J.

Use the equation for kinetic energy and solve for v:
The final speed is 20.0^{1/2} = 4.47 m/s.

Practice questions

You’re applying 600.0 N of force to a car with a mass of 1,000.0 kg. You’re traveling a distance of 100.0 m on a frictionless, icy road. What is the car’s final speed?

You’re ice skating and traveling at 30.0 m/s. If your mass is 65 kg, what is your kinetic energy?

You’re traveling in a car at 88 m/s. If you have a mass of 80.0 kg and the car has a mass of 1,200.0 kg, what is the total kinetic energy of you and the car combined?

You’re applying 3,000.0 N of force to a hockey puck with a mass of 0.10 kg. It travels over a distance of 0.10 m on a frictionless ice rink. What is the puck’s final speed?
Following are answers to the practice questions:

11 m/s

Find the total work done:
(600 N)(100 m) = 6.0 x 10^{4} J

The work done on the car goes into its kinetic energy, so its final kinetic energy is 6.0 x 10^{4} J.

Use the equation for kinetic energy and solve for v:

Plug in the numbers:
The final speed = 120^{1/2} = 11 m/s.


2.9 x 10^{4} J

The equation for kinetic energy is

Plug in the numbers:


4.9 x 10^{6} J

The equation for kinetic energy is

Plug in the numbers:


77 m/s

Find the total work done:
(3,000 N) (0.10 m) = 300 J

The work done on the puck goes into its kinetic energy, so its final kinetic energy is 300 J.

Use the equation for kinetic energy and solve for v:

Plug in the numbers:
The final speed = 6,000^{1/2} = 77 m/s.
