 # 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. 2. (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
$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{5-20}{4-0}\\ =-\frac{15}{4}{\text{ms}}^{-2}←\overline{)\begin{array}{l}\text{Negative gradient indicates}\\ \text{that the speed is decreasing}\text{.}\end{array}}\end{array}$
$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{10-5}{5-4}\\ =5{\text{ms}}^{-2}\end{array}$