# Gradient and Area Under a Graph Long Questions (Question 5 & 6)

Question 5:

The diagram above shows the speed-time graph of a moving object for 15 seconds. Find
(a)    the speed of the object at t = 9s.
(b)   the distance travel by the object for the first 12 seconds.

Solution:

(a)
The speed of the object at t = 9s is 6 ms-1

(b)
Distance travel by the object for the first 12 seconds
= Area under the speed-time graph
= Area of triangle
= ½ × 12 × 8
= 48 m

Question 6:

The diagram above shows the speed-time graph of a moving object for 15 seconds.
(a) Find the time interval when the object moves with constant speed.
(b)   Find the acceleration from t = 6s to t = 12s.
(c) State the time when the object is stationary.

Solution:

(a)
Time interval when the object moves with constant speed
= 12 – 6
= 6 s

(b)
$\begin{array}{l}\text{Acceleration from}t=6s\text{to}t=12s\\ =\text{Gradient of speed-time graph}\\ =\frac{6-6}{12-6}\\ =0{\text{ms}}^{-2}←\overline{)\begin{array}{l}\text{The moving object is moving}\\ \text{at a uniform speed}\end{array}}\end{array}$

(c)

Time when the object is stationary is at 15s.