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

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(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
= Gradient
= y 2 − y 1 x 2 − x 1 = 5 − 20 4 − 0 = − 15 4 ms − 2 ← Negative gradient indicates that the speed is decreasing .

(b)
Rate of speed change when the car travels from Y to Z
= Gradient
= y 2 − y 1 x 2 − x 1 = 10 − 5 5 − 4 = 5 ms − 2