Motion — OCR GCSE Physics

Acceleration measures how quickly velocity changes, so it is the change in velocity divided by the time taken for that change. Find the change in velocity by subtracting the initial velocity from the final velocity, keeping direction in mind: a car slowing from 20 m/s to 8 m/s in 6 s has a change of 8 − 20 = −12 m/s, giving a = −12 ÷ 6 = −2 m/s², a deceleration. Units follow from the division: (m/s) ÷ s = m/s². Rearranged forms are a × t = Δv and t = Δv ÷ a. In a multiple-choice question, compute the value first, then check the unit and sign before matching an option, since distractors often divide by the wrong quantity or drop the negative sign.

This equation links velocity, acceleration and distance for motion with constant acceleration, without needing the time. Square the final velocity and subtract the square of the initial velocity; this equals twice the acceleration multiplied by the distance travelled. For example, a cyclist accelerating at 2 m/s² from rest over 9 m reaches v² = 0² + 2 × 2 × 9 = 36, so v = 6 m/s. To find distance, divide the difference of the squared velocities by twice the acceleration. Check units: (m/s)² and m/s² × m both give m²/s². In a multiple-choice question, square the velocities before subtracting, then take the square root if the option is a velocity rather than a squared value.

Kinetic energy is the energy a moving object stores because of its motion, measured in joules (J). The equation is Eₖ = ½ × m × v², where m is mass in kilograms and v is speed in metres per second. Because speed is squared, doubling the speed multiplies kinetic energy by four, while doubling the mass only doubles it. Worked example: a 2 kg trolley moving at 3 m/s has Eₖ = ½ × 2 × 3² = ½ × 2 × 9 = 9 J. Convert grams to kilograms by dividing by 1000, and convert km/h to m/s by dividing by 3.6 before squaring. Always square the speed first, then multiply by mass, then halve.

Measuring motion means choosing a method that suits the scale and setting. For a trolley on a bench, use a metre rule or tape for distance and light gates or a stopwatch for time. For a falling object, use a ruler or metre rule for drop height and light gates or a slow-motion camera for short time intervals. For a runner on a track, use a tape or marked track for distance and a stopwatch or timing gates for time. For a toy car down a ramp, mark start and finish lines, measure the length with a tape, and time with a stopwatch or light gates. Match the instrument to the quantity, repeat readings, and reduce reaction-time error by using electronic timing where possible.

Speed is distance travelled divided by time taken, so a measurement needs both a length and a timing. Measure distance with a metre rule or tape measure, choosing a straight run between two clear marks, and measure time with a stopwatch started and stopped at those marks. Repeat and average to reduce random error. On a distance–time graph, speed is the gradient: pick two points on a straight section, read the change in distance and the change in time, then divide. A steeper line means greater speed; a horizontal line means the object is stationary. On a speed–time graph, distance travelled is the area under the line. Convert units before dividing so the answer is in m/s.

This criterion asks you to use ratios and proportional reasoning in two ways: converting between units and computing rates. For unit conversion, build a ratio from known equivalences, such as 1 km = 1000 m or 1 hour = 3600 s, and multiply or divide by that factor. For example, 72 km/h becomes 72 × 1000 ÷ 3600 = 20 m/s. For rates, identify which quantity is divided by which: speed is distance ÷ time, so doubling the distance while time stays fixed doubles the speed, but doubling the time while distance stays fixed halves the speed. Reason about direction and size before calculating, then check the answer's units and magnitude.

A scalar has magnitude only; a vector has magnitude and direction. Distance is the total length of the path travelled and is a scalar, so walking 3 m east then 4 m west gives a distance of 7 m. Displacement is the straight-line change in position from start to finish, with direction, so the same walk gives a displacement of 1 m west. Speed is the scalar rate of covering distance, while velocity is the vector rate of change of displacement, so a car going round a bend at constant speed still changes velocity because its direction changes. In multiple-choice questions, decide first whether the quantity needs a direction, then check the units and wording before choosing the option.

Choose the graph that matches the motion described. On a distance-time graph the slope gives speed: a horizontal line means the object is stationary, a straight sloping line means constant speed, and a steeper line means greater speed. On a velocity-time graph the slope gives acceleration: a horizontal line means constant velocity, a rising line means acceleration and a falling line means deceleration, while the area under the line gives the distance travelled. A curved line on either graph shows changing speed or changing acceleration. In multiple-choice questions, match each feature of the described motion, such as rest, steady speed, speeding up or slowing down, to the correct line shape and slope on the right type of graph.

On a velocity-time graph the velocity axis is vertical and time is horizontal. Splitting the region between the plotted line and the time axis into rectangles and triangles lets you find the enclosed area, and because velocity multiplied by time gives displacement, that area represents the displacement travelled in the chosen time interval. For a car accelerating steadily from rest to 20 m/s over 10 s, the area is a triangle: ½ × 10 s × 20 m/s = 100 m. For motion above the axis the displacement is positive; a region below the axis gives negative displacement, so areas on opposite sides must be subtracted to find the resultant displacement. Higher tier learners must read values from the axes, choose the correct shapes, keep units consistent and state what the area means rather than only a number.

Non-uniform motion means the speed changes during a journey, so a single instantaneous speed does not describe the whole trip. Average speed is found by dividing the total distance travelled by the total time taken: average speed = total distance ÷ total time. For example, a cyclist covering 300 m in the first 20 s and 500 m in the next 40 s travels 800 m in 60 s, giving an average speed of about 13.3 m/s. Use the whole journey, not one stage, and convert mixed units such as minutes to seconds and kilometres to metres before dividing. The answer describes overall motion and does not claim the object moved at that speed throughout.

This criterion asks you to select and use the right relationship for two different kinds of motion. For uniform motion, speed stays constant, so distance = speed × time, rearranged as speed = distance ÷ time or time = distance ÷ speed. For motion with uniform acceleration, speed changes at a steady rate, so distance = average speed × time, where average speed = (initial speed + final speed) ÷ 2. You also use acceleration = change in speed ÷ time and the combined relationship linking final speed, initial speed, acceleration and distance. In a multiple-choice question, read which quantities are given, decide whether speed is constant or changing, then pick the formula that uses exactly those quantities. Check units: convert minutes to seconds and kilometres to metres before substituting.

In motion practicals you choose apparatus matched to each quantity and record readings accurately. Measure length with a ruler or tape measure, reading at eye level to avoid parallax. Find area by measuring suitable lengths and calculating, for example length × width for a rectangle, keeping units consistent. Measure mass with a balance, time with a stopwatch or light gate, volume with a measuring cylinder read at the meniscus, and temperature with a thermometer allowed to reach steady reading. Accuracy means choosing apparatus with suitable resolution, repeating readings where sensible, and recording values with correct units and an appropriate number of significant figures. You should also consider how to reduce error, such as timing several oscillations and dividing, or using a fiducial marker.

This practical activity requires you to choose apparatus that suits the motion being studied and to use it so that speed and the rate of change of speed can be found. For steady motion over a measured distance, use a metre rule or tape to measure the distance and a stopwatch or light gates to measure the time; speed equals distance divided by time. For changing motion, light gates at two points give the speed at each point, and dividing the change in speed by the time between the gates gives acceleration or deceleration. A ticker-timer or a video with frame analysis can also record position at equal time intervals. Record repeat readings, keep units consistent and identify whether the value is speeding up or slowing down.