Calculating Kinetic Energy

Kinetic energy is the energy stored in a moving object. It depends on the object’s mass and the square of its speed.

The equation

$E_k = \frac{1}{2}mv^2$

Symbol	Quantity	Unit
$E_k$	Kinetic energy	J
$m$	Mass	kg
$v$	Speed	m/s

Key features

• Kinetic energy is proportional to $v^2$. Doubling the speed quadruples the kinetic energy.
• A heavier object moving at the same speed has more kinetic energy.

Worked example

Calculate the kinetic energy of a 1200 kg car travelling at 25 m/s.

$E_k = \frac{1}{2} \times 1200 \times 25^2 = \frac{1}{2} \times 1200 \times 625 = 375\,000\text{ J} = 375\text{ kJ}$

Worked example: finding speed

A 0.50 kg ball has 16 J of kinetic energy. Calculate its speed.

$v = \sqrt{\frac{2E_k}{m}} = \sqrt{\frac{2 \times 16}{0.50}} = \sqrt{64} = 8.0\text{ m/s}$

Common errors and how to correct them

Forgetting to square the velocity. The equation uses $v^2$, not $v$. A common error is to calculate $\frac{1}{2} \times m \times v$ instead.

Confusing speed and velocity. Kinetic energy uses speed (the scalar), not velocity. Since $v$ is squared, the direction does not affect the result. This also means kinetic energy is always positive.

How to apply this in an exam

Show the equation, substitute values, and keep units consistent (kg and m/s give joules). When rearranging for $v$, remember to take the square root at the end.