Distance-time graphs show how the distance travelled by a moving object changes with time.

Part of

Describe this journey in as much detail as possible.

Give values for velocities, acceleration and displacements.

- Question
Describe the motion of the car during the first 20 s.

The car has an initial velocity of 12 m/s.

From 0 to 20 seconds it moves at a constant velocity of 12 m/s.

- Question
What is the displacement of the car after 20 s?

In 20 s the displacement of the car is equal to the area of the rectangle.

Displacement = area of rectangle = 20 s × 12 m/s = 240 m.

- Question
Calculate the deceleration of the car from 20 s to 30 s.

At 30 seconds the car stops, its velocity is 0 m/s.

Acceleration of the car is the gradient of the graph =

acceleration = (0 m/s – 12 m/s) ÷ 10 s = -1.2 m/s

^{2}The car has an acceleration of -1.2 m/s

^{2}(or a retardation of 1.2 m/s^{2}).

- Question
How far does the car move while decelerating?

The displacement while decelerating equals the area of triangle

displacement = 10 s x 12 m/s = 60 m

The car moves 60 m while decelerating.

- Question
What is the average velocity of the car during its entire journey?

The total displacement of the car = total area under the graph = 240 m + 60 m = 300 m.

The average velocity of the car over the whole journey =

average velocity = 300 m ÷ 30 s = 10 m/s.

The average velocity of the car is 10 m/s.