The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

Displacement is the distance from the starting point when measured in a straight line.

Distance-time graphs

Maths

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.

Real-life graphs

This is a distance-time graph for a journey. What was the total distance travelled?

This is a displacement-time graph for a journey. How far was travelled in total? 

Here is a distance-time graph for a race car driving on a straight track. How fast is the car going?

What speed is the object travelling at between 4 and 6 hours? Give your answer in km/h.

The distance-time graph shows a two stage journey of an object. What is the average speed of this object? 

The average speed for this journey is {{}} km/h.

What number is the arrow pointing to on this number line? 

Here is a distance-time graph for a journey. How far had been travelled after 1 hour? 

Here is a distance-time graph for a journey. How far had been travelled after 3 hours?  

Moving away from the fixed start point at a constant speed.

Moving towards the fixed start point at a constant speed.

On this displacement-time graph what does the line segment marked a) represent? 

Starter Quiz