# Rates of Change of Distance - Time Graphs

- Author:
- Mr Malkin

A set of graphs allowing us to look at chords and tangents to curves, interpreting the gradients of these as average and instantaneous rates of change.
Use the orange slider to change the graph between six presets. (It takes a little time to switch between the graphs: be patient.)
Think about:
- gradient
- rates of change
- instantaneous vs average
- chords
- tangents
- velocity vs speed

**Questions:**- What does it mean when the graph is going downhill? - What does it mean when the graph is going uphill? - What does it mean when the graph is flat? - At what point is the car travelling fastest? - A what point is the car travelling slowest? - Find two different points where the car is travelling at the same velocity. - Choose two different points. Calculate the average speed of the car between these points by calculating displacement divided by time taken. - Choose two different points. Draw the chord between these points. Work out the gradient of this chord. - Switch to the straight line graph. Choose two points. Calculate the average speed of the car between these points. Choose a different two points. Calculate the average speed of the car between these points. Choose a different two points. Calculate the average speed of the car between these points. What do you notice? Can you explain? - Remain on the straight line graph. Choose one point. What is the velocity of the car at this point? - Switch to a curved graph. Choose one point. What is the velocity of the car at this point?