Speed is the rate at which something is moving. It is measured as the distance travelled per unit of time.

Acceleration is the rate of change of speed with respect to time.

Deceleration is the rate at which the speed of an object is decreasing.

Non-linear distance-time graphs

Maths

Checking and securing understanding of reading from context-based graphs

Checking and securing understanding of drawing distance-time graphs

Distance-time graphs

Speed-time graphs

Interpreting and drawing real-life graphs

Interpreting and drawing more real-life graphs

Calculating the rate of change

Estimating the gradient of a curve

Improving the estimate of the gradient of a curve

Finding the equation of a radius of a circle

Finding the equation of the tangent to a circle

Calculating journeys from linear speed-time graphs

Estimating journeys from non-linear graphs

Efficiently estimating journeys from non-linear graphs

Advanced problem solving with real-life graphs

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.

Real-life graphs

Slowest section of (non-zero) constant speed

This distance-time graph shows the journey of an object. Match up the stages of the graph labelled a)-e) with the stages of the journey.

Which of these is the correct distance-time graph for the journey shown on this speed-time graph?

Which of these is the correct speed-time graph for the journey shown on this distance-time graph?

Which of these graphs could show an object decelerating until stopped?

Which speed-time graph could show the same journey as this distance-time graph?

Which of these graphs show speed increasing (positive acceleration)?

This distance-time graph shows an object moving at constant speed. The object is travelling at {{}} m/s.

Horizontal line on a displacement-time graph.

Horizontal line on speed-time graph (not along the $$x$$-axis).

Diagonal line with positive gradient on a displacement-time graph.

Diagonal line with negative gradient on a displacement-time graph.

Diagonal line with positive gradient on a speed-time graph.

Which of these represents constant non-zero speed?

Travelling down hill at a constant speed.

Travelling towards a fixed start point at a constant speed.

Object has moved past the start point in the opposite direction.

What does a line segment with negative gradient represent on a speed-time graph?

The speed-time graph shows the first 20 seconds of an object's journey. How long was the object stationary during this time?

The speed-time graph shows the first 20 seconds of an object's journey. How long was the object decelerating for?

Starter Quiz

The gradient of this line is .