SP1 · Motion · Topic 2 — Motion and forces | GCSE Edexcel Separate Sciences

Revise the key ideas

A scalar has a size (magnitude) but no direction. Distance, speed, time, energy and mass are scalars.
A vector has both a size (magnitude) and a direction. Displacement, velocity, acceleration, force, weight and momentum are vectors.
Distance is the total path length. Displacement is the straight-line change from starting position to finishing position, with a direction.
A runner completing a 400 m lap travels 400 m but has zero displacement on returning to the start.
A complete lap has distance but no displacement.
Speed tells you how fast something moves. Velocity is speed in a stated direction: 5 m/s east differs from 5 m/s west.
Use SI units: distance in metres (m), time in seconds (s), speed in m/s and acceleration in m/s². Convert before substituting: 1 km = 1000 m; 1 hour = 3600 s.
Common prefixes include kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶) and nano (10⁻⁹). Keep suitable significant figures and use standard form for very large or small quantities.

Average speed = total distance ÷ total time. Rearrange to distance = speed × time and time = distance ÷ speed. Average velocity instead uses displacement divided by time.
A cyclist travels 120 m in 15 s: average speed = 120 ÷ 15 = 8 m/s. An average need not be the speed at every instant.
To measure average speed, measure a known distance and time the journey with a stopwatch. Repeat and calculate a mean; a longer measured distance reduces the relative effect of reaction-time uncertainty.
A light gate measures the time a card of known length blocks its beam: speed = card length ÷ interruption time. Two gates can measure speeds at separate positions.
Typical walking, running and cycling speeds are roughly 1.5, 3 and 6 m/s; values vary with person and conditions. Typical sound speed in air is about 330–340 m/s.
On a distance–time graph, the gradient is speed: choose two points and divide change in distance by change in time.
A horizontal distance–time line means stationary; a straight rising line means constant speed; a steeper rising line means greater speed. A curved line has a changing gradient and therefore changing speed.
Rising segment: 20 ÷ 4 = 5 m/s. Flat segment: stationary.

Acceleration = change in velocity ÷ time, a = (v − u)/t, with u initial velocity and v final velocity. Units are m/s².
Changing from 4 m/s to 16 m/s in 3 s gives a = (16 − 4) ÷ 3 = 4 m/s². A negative acceleration opposes the chosen positive direction.
An object can accelerate by changing speed or direction. Circular motion at constant speed still has changing velocity.
For an object falling freely near Earth, use acceleration g ≈ 10 m/s² for these GCSE examples. This assumes air resistance is negligible; follow any value supplied in a question.
For constant (uniform) acceleration, v² − u² = 2ax links initial velocity u, final velocity v, acceleration a and displacement x. You do not need to know the time. Keep units consistent.
Example: starting from rest with a = 2 m/s² over 25 m, v² = 2 × 2 × 25 = 100, so final speed is 10 m/s.
Use this equation only for constant acceleration.

The gradient of a velocity–time graph gives acceleration: Δv/Δt. A steeper gradient has a larger magnitude of acceleration.
A horizontal line means constant velocity, including rest if it lies on zero. A straight sloping line means uniform acceleration.
The area between a velocity–time graph and the time axis gives displacement. Count areas above the axis as positive and below it as negative. If velocity stays positive, this also gives distance travelled.
For a line below zero, velocity is in the negative direction. Add the magnitudes of positive and negative areas to calculate total distance, but subtract negative areas to calculate displacement.
A rectangle has area velocity × time; a triangle has area ½ × base × height. Add simple areas for a journey with different stages.
A vehicle accelerating uniformly from 0 to 12 m/s in 4 s travels ½ × 4 × 12 = 24 m. Its acceleration is 12 ÷ 4 = 3 m/s².
Triangle area gives distance; the slope gives acceleration.
Do not swap graph rules: distance–time gradient gives speed; velocity–time gradient gives acceleration; velocity–time area gives displacement.