Example

Describe this journey in as much detail as possible.

Give values for velocities, acceleration and displacements.

A velocity-time graph. The line is split into 2 parts. It starts at time 0 and velocity 12 and continues at the same velocity for 20 seconds. From 20 to 30 seconds the velocity decreases from 12 to 0.
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 =

\frac{\text{final velocity – initial velocity}}{\text{time taken}}

acceleration = (0 m/s – 12 m/s) ÷ 10 s = -1.2 m/s2

The car has an acceleration of -1.2 m/s2 (or a retardation of 1.2 m/s2).

Question

How far does the car move while decelerating?

The displacement while decelerating equals the area of triangle

displacement = \frac{\text{1}}{\text{2}} 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 = \frac{\text{total displacement}}{\text{time}}

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

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

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