For example, a car travels 300m in 20s.

Its speed is 300 ÷ 20 = 15m/s.

The vertical axis of a distance-time graph is the distance travelled from the start, and the horizontal axis is the time taken from the start.

Distance - time graph

Note that the steeper the line, the greater the speed of the object. The blue line is steeper than the red line because it represents an object moving faster than the object represented by the red line.

The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities. One velocity will be positive, and the velocity in the other direction will be negative.

Features of the graphs

When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a steadily increasing velocity, or a steadily decreasing velocity, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph

The steeper the line, the more rapidly the velocity of the object is changing

The green arrow shows the force on the weights as the weightlifter pushes upwards.

The red arrow shows the downwards force on the weightlifter’s arm muscles.

These two forces are an interaction pair. They are equal in size, and opposite in direction

A book on a table has a downwards force (its weight) due to gravity.

This downwards force, pushing on the table, produces an upwards force called reaction.

Reaction forces

Resultant force

The resultant force is the sum of all the different forces acting on the car.

• Gravity pulls down on the car.
• The reaction force from the road pushes up on the wheels.
• The driving force from the engine pushes the car along.
• There is friction between the road and the tyres.
• Air resistance acts on the front of the car.

counter forces of air resistance and friction pushing backwards.

You need to know how these forces compare if you are to predict what will happen to the speed of a moving object.

• If the driving force is greater than the counter forces, there is a resultant force forwards. This will make the car speed up.
• If the driving force is less than the counter forces, there is a resultant force backwards. This will make the car slow down.

If the driving force is the same as the counter forces, there is no resultant force, and so no change in velocity.

• If the car is already moving, it will carry on at a steady speed in a straight line.
• If the car is not moving, it will stay still.

The momentum of a moving object depends on its mass and its velocity:

momentum (in kg m/s) = mass (in kg) × velocity (in m/s)

The size of the change in momentum depends on the size of the resultant force and the time for which the force acts:

change of momentum (in kg m/s) = resultant force (in newton, N) × time for which it acts (in s).

Work and energy are measured in the same unit, the joule (J).

change in energy (joule, J) = work done (joule, J)

The equation

This equation shows the relationship between work done, force applied and distance moved:

work done (joules, J) = force (newtons, N) x distance (metres, m)

weight (newton, N) = mass (kilogram, kg) x gravitational field strength (N/kg)

The gravitational field strength on the Earth’s surface is about 10N/kg. This is quite handy because all you need to do to convert between weight and mass is to multiply the mass by 10.

For example, a 1kg bag of sugar weighs 1 × 10 = 10N.

change in GPE = weight x change in height

For example, if a 1N weight is raised by 5m it gains 1 × 5 = 5J of gravitational potential energy.

Kinetic energy (KE)

Every moving object has kinetic energy (KE). The more mass an object has and the faster it is moving, the more kinetic energy it has. So the bigger the object, the faster it will move.

This equation shows the relationship between kinetic energy (J), mass (kg) and speed (m/s):

kinetic energy = 1/2 × mass × speed²