### Distance time, velocity time graphs

Year 10/11 maths: Calculating gradients for speed and distance travelled from area under graph.

###### Basic distance-time graph.

This graph shows how an objects distance changes with time.

The gradient of the graph tells you the velocity or speed (m/s)

A velocity is a speed in a certain direction

Part A of the graph shows a velocity of 15m/5s = 3m/s

Q1: What velocity is shown by parts B, C and D?

ANS

###### Distance-time graph, speed change   More 1 More 2

This curved graph shows the distance a person travels in 30 seconds.

Q1: Work out the gradient at time = 15

Q2: Explain what the gradient of this tangent tells you about the person.

ANS

###### Velocity-time graph, constant acceleration

This graph is often called a speed time graph.

It shows how velocity changes with time.

The gradient of the graph is the acceleration, m/s2

Part A of the graph shows an acceleration of 15ms/5s = 3m/s2

Q1: What acceleration is shown by parts B and C?

Q2: What is the distance travelled

ANS

###### Velocity-time graph, distance travelled  More

This curved graph shows how the velocity of a car changes over 30 seconds.

Q1: Work out the gradient at time = 10

Q2: Explain what the gradient of this tangent tells you about the car.

Q3: How would you work out the distance travelled in 15 seconds

ANS