Using Force and Motion Equations in GCSE Physics

Use force and motion equations by identifying the quantities given, choosing an equation containing those quantities, rearranging it if necessary, and substituting values in standard units.

Assumption: this explanation is for AQA GCSE Physics at Higher tier. Most of these ideas also apply at Foundation tier.

Key equations

For motion at constant speed:

$$s=vt$$

where $s$ is distance in metres, $v$ is speed in metres per second and $t$ is time in seconds.

Acceleration is the change in velocity per unit time:

$$a=\frac{\Delta v}{t}=\frac{v-u}{t}$$

Here, $u$ is initial velocity, $v$ is final velocity and $\Delta v$ means change in velocity.

Newton’s Second Law links resultant force, mass and acceleration:

$$F=ma$$

The resultant force is the single overall force after forces acting in opposite directions have been combined.

For motion with constant acceleration, you may also use:

$$v^2-u^2=2as$$

A reliable method

1. Write down every value from the question, including its unit.
2. Convert values before substitution. For example, change minutes to seconds and grams to kilograms.
3. Choose an equation containing the quantity required and the quantities supplied.
4. Rearrange using symbols first. This reduces calculator errors and makes your method clear.
5. Substitute the values, calculate, then give the answer with the correct unit.

When forces oppose, subtract the smaller force from the larger one. When they act in the same direction, add them before using $F=ma$.

Worked example

A car of mass $1200kg$ increases its velocity from $5m/s$ to $15m/s$ in $4s$. Calculate the resultant force.

First calculate acceleration:

$$a=\frac{v-u}{t}=\frac{15-5}{4}=2.5{m/s}^2$$

Then use $F=ma$:

$$F=1200\times 2.5=3000N$$

Therefore, the resultant force is $3000N$.

Exam mistake to avoid

Do not substitute every force separately into $F=ma$. The force in this equation is the resultant force. Also check units before calculating: mass should be in kilograms, time in seconds and distance in metres. Remember that speed has no direction, whereas velocity includes direction, so a change in direction is a change in velocity even if speed stays constant.