Kinetic Energy (AQA GCSE Combined Science: Trilogy: Physics): Revision Note

Calculate the kinetic energy stored in a vehicle of mass 1200 kg moving at a speed of 27 m/s.

Answer:

Step 1: List the known quantities

• Mass of the vehicle, m = 1200 kg

• Speed of the vehicle, v = 27 m/s

Note: Both values are already in the units the equation needs (kg and m/s), so no conversions are needed

Step 2: Write down the equation for kinetic energy

• This equation is given on the Physics Equations Sheet

$E_k=\frac{1}{2}\times m\times v^2$

Step 3: Substitute the known values and calculate the kinetic energy

• Square the speed first, then multiply by the mass and by ½

$E_k=\frac{1}{2}\times 1200\times {27}^2$

$E_k=\frac{1}{2}\times 1200\times 729$

$E_k=437 400\text{ J}$

Step 4: Round the final answer to 2 significant figures

• The input values are given to 2 significant figures, so the answer can only be given to the same degree of accuracy

$E_k=440 000\text{ J}$

A skateboarder has a kinetic energy of 270 J and a speed of 3.0 m/s. Calculate the mass of the skateboarder.

Answer:

Step 1: List the known quantities

• Kinetic energy, E_k = 270 J

• Speed, v = 3.0 m/s

Step 2: Write down the equation for kinetic energy

$E_k=\frac{1}{2}\times m\times v^2$

Step 3: Rearrange the equation to make mass the subject

• Multiply both sides by 2:

$2\times E_k=m\times v^2$

• Divide both sides by v²:

$m=\frac{2\times E_k}{v^2}$

Step 4: Substitute the known values and calculate the mass

• Remember to square the speed before you divide

$m=\frac{2\times 270}{3.0^2}$

$m=\frac{540}{9.0}$

$m=60\text{ kg}$

When performing calculations using the kinetic energy equation, always double-check that you have squared the speed. Forgetting to do this is the most common mistake that students make. Two other common slips are leaving out the ½ and writing kinetic energy as mass × speed. The equation is given on the Physics Equations Sheet, so copy it carefully.

• Always square the speed before you multiply by the mass

• Do not leave out the ½ and do not use E_k = m × v

• If the question gives you the kinetic energy, substitute it into the equation and solve for the unknown

• Check the unit of each value before you substitute