Kinetic energy

Energy

GCSE Physics (8463)

ORIGINAL

Find the kinetic store at each speed, then subtract — never square the change in speed.

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Question

A cyclist and her bicycle have a combined mass of

80\,\text{kg}

. She speeds up from

4.0\,\text{m/s}

9.0\,\text{m/s}

. Calculate the increase in the energy in the kinetic energy store of the cyclist and bicycle.

Every step worked, with the reasoning.

1
$E_k = \tfrac{1}{2}mv^2$ , with $m = 80\,\text{kg}$
Kinetic energy depends on speed squared, so work out the store at each speed separately.
2
Before: $E_k = \tfrac{1}{2} \times 80 \times 4.0^2 = 640\,\text{J}$
Square the speed first: $4.0^2 = 16$ , then $0.5 \times 80 \times 16 = 640$ .
3
After: $E_k = \tfrac{1}{2} \times 80 \times 9.0^2 = 3240\,\text{J}$
$9.0^2 = 81$ , then $0.5 \times 80 \times 81 = 3240$ .
4
Increase $= 3240 - 640 = 2600\,\text{J}$
The increase in the store is the final value minus the initial value; the data are given to 2 significant figures, and so is $2600\,\text{J}$ .

Answer: $2600\,\text{J}$ ( $2.6\,\text{kJ}$ )