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Welcome to GCSE Edexcel Science revision.

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Unit S P 1: Motion.

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A scalar has a size (magnitude) but no direction.

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Distance, speed, time, energy and mass are scalars.

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A vector has both a size (magnitude) and a direction.

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Displacement, velocity, acceleration, force, weight and momentum are vectors.

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Distance is the total path length.

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Displacement is the straight-line change from starting position to finishing position, with a direction.

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A runner completing a 400 metres lap travels 400 metres but has zero displacement on returning to the start.

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A complete lap has distance but no displacement.

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Speed tells you how fast something moves.

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Velocity is speed in a stated direction: 5 metres per second east differs from 5 metres per second west.

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Use S I units: distance in metres, time in seconds, speed in metres per second and acceleration in metres per second squared.

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Convert before substituting: 1 kilometre equals 1000 metres; 1 hour equals 3600 seconds.

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Common prefixes include kilo,

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ten to the power three;

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centi,

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ten to the power minus two;

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milli,

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ten to the power minus three;

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micro,

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ten to the power minus six;

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and nano,

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ten to the power minus nine.

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Keep suitable significant figures and use standard form for very large or small quantities.

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Average speed equals total distance divided by total time.

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Rearrange to distance equals speed times time and time equals distance divided by speed.

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Average velocity instead uses displacement divided by time.

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A cyclist travels 120 metres in 15 seconds: average speed equals 120 divided by 15 equals 8 metres per second.

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An average need not be the speed at every instant.

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To measure average speed, measure a known distance and time the journey with a stopwatch.

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Repeat and calculate a mean; a longer measured distance reduces the relative effect of reaction-time uncertainty.

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A light gate measures the time a card of known length blocks its beam: speed equals card length divided by interruption time.

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Two gates can measure speeds at separate positions.

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Typical walking, running and cycling speeds are roughly 1.5, 3 and 6 metres per second; values vary with person and conditions.

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Typical sound speed in air is about 330 to 340 metres per second.

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On a distance, time graph, the gradient is speed: choose two points and divide change in distance by change in time.

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A horizontal distance, time line means stationary; a straight rising line means constant speed; a steeper rising line means greater speed.

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A curved line has a changing gradient and therefore changing speed.

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Rising segment: 20 divided by 4 equals 5 metres per second.

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Flat segment: stationary.

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Acceleration equals change in velocity divided by time, A equals the quantity V minus U, divided by T, with U initial velocity and V final velocity.

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Units are metres per second squared.

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Changing from 4 metres per second to 16 metres per second in 3 seconds gives A equals (16 minus 4) divided by 3 equals 4 metres per second squared.

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A negative acceleration opposes the chosen positive direction.

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An object can accelerate by changing speed or direction.

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Circular motion at constant speed still has changing velocity.

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For an object falling freely near Earth, use acceleration G approximately equals 10 metres per second squared for these GCSE examples.

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This assumes air resistance is negligible; follow any value supplied in a question.

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For constant (uniform) acceleration, V squared minus U squared equals two times A times X links initial velocity U, final velocity V, acceleration A and displacement X.

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You do not need to know the time.

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Keep units consistent.

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Example: starting from rest with A equals 2 metres per second squared over 25 metres, V squared equals 2 times 2 times 25 equals 100, so final speed is 10 metres per second.

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Use this equation only for constant acceleration.

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The gradient of a velocity, time graph gives acceleration: change in velocity divided by change in time.

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A steeper gradient has a larger magnitude of acceleration.

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A horizontal line means constant velocity, including rest if it lies on zero.

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A straight sloping line means uniform acceleration.

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The area between a velocity, time graph and the time axis gives displacement.

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Count areas above the axis as positive and below it as negative.

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If velocity stays positive, this also gives distance travelled.

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For a line below zero, velocity is in the negative direction.

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Add the magnitudes of positive and negative areas to calculate total distance, but subtract negative areas to calculate displacement.

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A rectangle has area velocity times time; a triangle has area one half times base times height.

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Add simple areas for a journey with different stages.

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A vehicle accelerating uniformly from 0 to 12 metres per second in 4 seconds travels one half times 4 times 12 equals 24 metres.

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Its acceleration is 12 divided by 4 equals 3 metres per second squared.

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Triangle area gives distance; the slope gives acceleration.

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Do not swap graph rules: distance, time gradient gives speed; velocity, time gradient gives acceleration; velocity, time area gives displacement.

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That completes Motion.

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Revisit the notes and test yourself on the revision website.