Newton's three laws of motion applied to sport, the definitions and relationships of the linear motion quantities, and the interpretation of motion graphs.

What this dot point is asking

WJEC wants you to state and apply Newton's three laws of motion to sporting situations, define the linear motion quantities and their relationships (including momentum), and interpret distance-time and velocity-time graphs.

Newton's three laws of motion

Applied to a sprinter: in the blocks they stay still (inertia) until they push; the force their legs apply produces an acceleration in proportion to that force and inversely to their mass ($F = ma$); and as they push back and down on the blocks, the blocks push them forward and up with an equal and opposite ground reaction force.

Linear motion quantities

The key relationships are: $\text{speed} = \dfrac{\text{distance}}{\text{time}}$, $\text{velocity} = \dfrac{\text{displacement}}{\text{time}}$, $\text{acceleration} = \dfrac{\text{change in velocity}}{\text{time}}$, and $\text{momentum} = \text{mass} \times \text{velocity}$. Momentum is conserved in collisions, which is why a heavier or faster player is harder to stop.

Interpreting motion graphs

• On a distance-time (or displacement-time) graph, the gradient gives the speed (or velocity): a steeper line means faster motion, a horizontal line means stationary.
• On a velocity-time graph, the gradient gives the acceleration (a positive slope is speeding up, a negative slope is slowing down), and the area under the line gives the distance travelled.

Examples in context

Example 1. The high-jump take-off. At take-off a high jumper drives down hard into the ground; by Newton's third law the ground pushes back with an equal and opposite force that lifts them upward. A greater downward force gives a greater upward reaction and a higher jump.

Example 2. Momentum in a tackle. A small, fast winger and a large, slower forward can carry similar momentum because momentum depends on both mass and velocity. WJEC uses this to show why the equation, not mass alone, decides who is harder to stop.

Try this

Q1. State Newton's first law of motion. [1 mark]

• Cue. A body remains at rest or in uniform motion in a straight line unless acted on by a resultant external force.

Q2. Explain how Newton's second law applies to throwing a shot put. [3 marks]

• Cue. The acceleration of the shot is proportional to the force applied and inversely proportional to its mass ($F = ma$); a greater force on the shot produces greater acceleration and release velocity.

Q3. On a velocity-time graph, state what the gradient and the area under the line represent. [2 marks]

• Cue. The gradient represents acceleration; the area under the line represents the distance travelled.