7.1.1 Quantity Represented by the Gradient of a Graph (Part 1)

7.1 Quantity Represented by the Gradient of a Graph

The gradient of graph is the rate of change of a quantity on the vertical axis with respect to the change of another quantity on the horizontal axis.

(A) Distance – Time Graph

1. The gradient of a distance-time graph is speed.

(a) From O to P: Gradient = positive

(b) From P to Q: Gradient = 0 → (The object stopped moving)

(c) From Q to R: Gradient = negative → (The object is travelling in an opposite direction from the original direction).

Example 1:

The diagram above shows a graph of distance-time for the motion of a car. Find the speed of the car for the first 6 second.

Solution:

The speed of the car for the first 6 seconds

= Gradient

\begin{array}{l} = \frac{12 - 0}{6 - 0} \\ = 2.0 {ms}^{- 1} \end{array}