Graphical Method

Graphical Method

The movement of a body takes place over time. The speed and direction can change in many ways. It is often convenient to represent the displacement, speed, velocity or acceleration as a graph against time.

For example, suppose a body moves at a uniform (constant, not changing) velocity. Suppose that the displacement d is 0 m when the time t is 0 s. Suppose that when t is 1 s, the body moves by 5 cm. When t is 2 s, the body moves by another 5 cm, and so on. A graph of the d versus t would then be a straight line. The velocity v is always 5 cm/s. So a graph of v against t would be a horizontal line. The graphs give a quick way to tell what type of motion is taking place.

What is the body is accelerating? Consider the case when the acceleration a is uniform (again, constant and not changing). This means that the velocity v increases by the same amount every second. Suppose v is zero when t is 0, 2 cm/s when t is 1 s, 4 cm/s when t is 2 s, and so on. A graph of v against t would be a straight line. Since a is constant, the graph of a versus t is a horizontal line.

This time, the displacement-time graph is not a straight line. The reason is that d does not increase by the same amount every second. It increases by a larger and larger amount with every passing second. So the graph is a curve that gets steeper and steeper with time.

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