7.1.2 Quantity Represented by the Gradient of a Graph (Part 2)

(B) Speed – Time Graph

1. The gradient of a speed-time graph is the rate of change of speed or acceleration.

(a) From O to P: Gradient = positive → (Speed of object increasing or accelerating).

(b) From P to Q: Gradient = 0 → (Object is moving at uniform speed).

(c) From Q to R: Gradient = negative → (Speed of object decreasing or decelerating).

Example:

The diagram above shows the speed-time graph of a moving car for 5 seconds. Find

(a) the rate of speed change when the car travel from X to Y.

(b) the rate of speed change when the car travel from Y to Z.

Solution:

(a)

Rate of speed change when the car travels from X to Y

= Gradient

\begin{array}{l} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ = \frac{5 - 20}{4 - 0} \\ = - \frac{15}{4} {ms}^{- 2} \leftarrow \begin{array}{l} Negative gradient indicates \\ that the speed is decreasing . \end{array} \end{array}

(b)

Rate of speed change when the car travels from Y to Z

= Gradient

\begin{array}{l} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ = \frac{10 - 5}{5 - 4} \\ = 5 {ms}^{- 2} \end{array}