The Kinetic Energy Equation

Kinetic energy equals one-half times mass times the square of the velocity.

Just like with work, the units of kinetic energy can be derived directly from the following equation:

KE = 1 2 mv²

Units of KE = kg(m/s)² = kgm²/s² = (kg * m/s²)m = Nm = J

Practice Problems

Calculate the kinetic energy in the practice problems below. The first problem is an example.

Example

A physics teacher exerts a force on a 6.36 kg bowling ball that causes the ball to move horizontally at 2.55 m sec. Calculate the kinetic energy of the bowling ball. Identify all given information, and verify that measurements are in the correct units.

kinetic energy = ?     mass = 6.36 kg     velocity = 2.55 m sec

The correct formula for this problem isKinetic Energy equals one-half times mass times the velocity squared which equals one half times 6.36 kg times the square of 2.55 meters per second. KE = 1 2 mv²

KE = 1 2 mv² = ( 1 2 )(6.36 kg)(2.55 m sec)²
      = 8.109 20.68 kg * m² sec²
      = 20.68 J

Now you try! Refer to math help for assistance, or click on the "hint" buttons below for clues.

Practice Problem 1

What is the kinetic energy of a 90 kg football player running at 7 m/s?

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Hint 1

Identify all given information, and verify that measurements are in the correct units.

kinetic energy = ?     mass = 90 kg     velocity = 7.00 m/s

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Hint 2

The correct formula for this problem is KE = 1 2 mv².

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Solution

Kinetic Energy equals one-half times mass times the velocity squared which equals one half times 90 times the square of seven. Kinetic energy equals one-half times 90 times 49.
KE = 1 2 mv²
KE = 1 2 (90)(7)²
KE = 1 2 (90)(49)
KE = 2205J = 2210J (correct number of significant figures)

Practice Problem 2

What is the velocity of a truck that has a mass of 2568 kg and 4.320 * 10⁵J of kinetic energy?

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Hint 1

Identify all given information, and verify that measurements are in the correct units.

kinetic energy = 4.320 * 10⁵J     mass = 2468 kg     velocity = ?

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Hint 2

The correct formula for this problem is Kinetic Energy equals one-half times mass times the velocity squared. KE = 1 2 mv².

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Solution

Kinetic energy equals one-half times mass times the square of the velocity. Rearrange the equation to solve for v, where velocity equals the square root of the quanity two times the kinetic energy divided by the mass. V equals the square root of the quantity two times 4.320 times 10 to the fifth power joules divided by 2468 kilograms. Velocity equals 18.71 meters per second (answer in correct number of significant figures). KE = 1 2 mv²

Rearrange the equation to solve for v:
2KE = mv²

2KE m = v²

√ 2KE m = v

v = √ (2)(4.320 X 10⁵ J) 2468 kg

v = 18.71 m sec
(answer in correct number of significant figures)