P3.1 Acceleration · KS3 Science

Scalars and vectors

A scalar has size only: distance, speed, mass, time, energy and temperature.
A vector has size and direction: displacement, velocity, force, acceleration and weight. Velocity is speed in a given direction.
Forces at right angles combine like the sides of a right-angled triangle: 3 N and 4 N at 90° give a resultant of 5 N. A single force can also be resolved (split) into two parts at right angles, using a scale drawing.

First law: if the resultant force on an object is zero, it stays still, or keeps moving at the same velocity.
Second law: resultant force = mass × acceleration (F = m × a). A 1000 kg car accelerating at 2 m/s² needs a resultant force of 2000 N.
Third law: when two objects interact, they exert equal and opposite forces on each other. A rocket pushes gas down, and the gas pushes the rocket up.

Acceleration = change in velocity ÷ time taken. It is measured in metres per second squared (m/s²).
A car that speeds up from 0 to 20 m/s in 10 s has an acceleration of 20 ÷ 10 = 2 m/s². Slowing down is a negative acceleration (deceleration).
The same force gives a smaller acceleration to a bigger mass.
To investigate acceleration, pull a trolley along a runway with hanging masses and measure its speed with light gates, which avoid human reaction-time errors.

A horizontal line means a constant velocity.
A straight line sloping upwards means a constant acceleration; sloping downwards means a constant deceleration.
The gradient (steepness) of the line is the acceleration.
The area under the line is the distance travelled: a car at 15 m/s for 20 s travels 15 × 20 = 300 m.

Scalar: A quantity with size only, such as speed.
Vector: A quantity with size and direction, such as velocity.
Displacement: The distance moved in a particular direction.
Velocity: Speed in a particular direction.
Acceleration: The rate of change of velocity, measured in m/s².
Deceleration: Slowing down (a negative acceleration).
Resultant force: The single force that has the same effect as all the forces acting.
Inertia: The tendency of an object to keep doing what it is doing.
Newton's first law: With no resultant force, an object stays still or moves at a steady velocity.
Newton's second law: Resultant force = mass × acceleration.
Newton's third law: Interacting objects exert equal and opposite forces on each other.
Velocity-time graph: A graph showing how velocity changes over time.
Light gate: A sensor that times an object passing through a beam, to measure speed.