← Kinetic and gravitational potential energy

Solve the kinetic energy equation for speed or mass

A 3 kg exercise ball rolls across a gym floor carrying 54 J of kinetic energy.

No speed in sight. The lesson unwraps the measured joules to get it back.

Work the numbers first. Double the ball's 54 J: 54 × 2 = 108.

Divide by the 3 kg mass: 108 ÷ 3 = 36. That is the speed squared: v² = 36.

Find the number that multiplies by itself to give 36: 6 × 6 = 36, so v = 6. The ball rolls at 6 m/s.

The exercise ball, run backwardstepvaluedouble the energy: 54 × 2108divide by the mass: 108 ÷ 336v² = 36, and 6 × 6 = 36v = 6 m/s
Double, divide, square root: the speed comes back out.

Now the equation behind the moves. Doubling cleared the half, and dividing removed the mass: v² = 2 × KE ÷ m, then v is the square root.

The mass unwraps with no square root: m = 2 × KE ÷ v².

Two arrangements, one habit: double the energy first, then divide, and save any square root for last.
The two arrangementsto findusespeedv² = 2 × KE ÷ m, then the square rootmassm = 2 × KE ÷ v²
Two arrangements, one habit: double the energy first.

A 4 kg sled carries 200 J of kinetic energy. Calculate its speed.

Write down the values:

KE = 200 J, m = 4 kg, v = ?

Write down the equation:

v² = 2 × KE ÷ m

Double the energy: 200 × 2 = 400.

Substitute in the values, and calculate:

v² = 400 ÷ 4 = 100

v² = 100, and 10 × 10 = 100, so the sled's speed is 10 m/s.

A cart moving at 5 m/s carries 150 J of kinetic energy. Calculate its mass.

Write down the values:

KE = 150 J, v = 5 m/s, m = ?

Write down the equation:

m = 2 × KE ÷ v²

Double the energy: 150 × 2 = 300. The speed squared: 5 × 5 = 25.

Substitute in the values, and calculate:

m = 300 ÷ 25 = 12

The cart's mass is 12 kg.

Symbol keysymbolnameunitKEkinetic energyJmmasskgvspeedm/s
KE = ½mv², solved for whichever symbol is missing.

Talia knows a wagon's kinetic energy and its mass. Which expression gives the speed squared?

The same wagon: its kinetic energy is 160 J and its mass is 5 kg. Enter its speed in m/s.

A curling stone glides at 2 m/s carrying 38 J of kinetic energy. Enter its mass in kg.

Your turn

A 10 kg toolbox slides off a loading ramp carrying 245 J of kinetic energy. Enter its speed in m/s.

A loaded wheelbarrow moving at 6 m/s carries 234 J of kinetic energy. Enter its mass in kg.

Four vehicles approach a toll plaza. To compare them, calculate each kinetic energy. Which vehicle has the greatest kinetic energy?