# Gradient and Area Under a Graph Long Questions (Question 3 & 4)

Question 3:

The diagram above shows the speed-time graph of a moving particle for 10 seconds. From the graph above, find
(a) the total distance travel by the particle for the whole journey.
(b)   the average speed for the whole journey.

Solution:
(a)
Total distance travelled
= Area under the speed-time graph
= Area of triangle
= ½ × 15 × 10
= 75 m

(b)
Average speed for the whole journey
$\begin{array}{l}=\frac{\text{Total distance travelled}}{\text{Total time taken}}\\ =\frac{75}{10}\\ =7.5\text{}m{s}^{-1}\end{array}$

Question 4:

The diagram above shows the speed-time graph of a moving particle for 12 seconds. Find
(a) the length of the time, in s that the particle move with uniform speed.
(b)   the distance travel by the particle when it move with constant speed.
(c)  the distance travel by the particle when the rate of the speed change is negative.

Solution:

(a)
Length of the time the particle move with uniform speed
= 10 – 6
= 4 s

(b)

Distance travel by the particle when it move with constant speed
= Area under the speed-time graph
= Area of rectangle
= 4 × 10
= 40 m

(c)
Distance travel by the particle when the rate of the speed change is negative
= Area under the speed-time graph for the first 6 s
= Area of trapezium
= ½ (10 + 25)(6)
= 105 m