Motion: displacement, velocity and acceleration, motion graphs and their gradients and areas, the equations of motion for uniform acceleration, and free fall under gravity.

What this dot point is asking

OCR wants you to define displacement, velocity and acceleration, interpret displacement-time and velocity-time graphs through their gradients and areas, apply the four equations of motion for uniform acceleration, and treat free fall as motion with acceleration $g$.

The answer

Displacement, velocity and acceleration

Motion graphs

Reading a graph is often quicker and safer than algebra. The area under a velocity-time graph can be split into triangles and rectangles, and the gradient of a tangent gives acceleration even when the motion is non-uniform.

The equations of motion

These equations apply only while the acceleration is constant. List the known quantities with a consistent sign convention (often taking the initial direction as positive), then pick the equation that fits.

Free fall

Examples in context

Stopping-distance calculations for road safety combine a constant-speed thinking phase with a constant-deceleration braking phase. Lift and crane motion is modelled as constant-acceleration segments joined to constant-velocity sections. Sports science uses velocity-time graphs to find an athlete's acceleration phase. Free-fall reasoning explains why astronauts appear weightless in orbit: they and their spacecraft fall together at the same $g$.

Try this

Q1. State what the gradient of a velocity-time graph represents. [1 mark]

• Cue. The acceleration.

Q2. A train decelerates uniformly from $30\ \text{m s}^{-1}$ to rest in $12\ \text{s}$. Find its deceleration. [2 marks]

• Cue. $a = \frac{v - u}{t} = \frac{0 - 30}{12} = -2.5\ \text{m s}^{-2}$.

Q3. An object falls freely from rest for $2.0\ \text{s}$. Find its speed and the distance fallen ($g = 9.81\ \text{m s}^{-2}$). [2 marks]

• Cue. $v = gt = 19.6\ \text{m s}^{-1}$; $s = \frac{1}{2}gt^2 = 19.6\ \text{m}$.