# Gradient and Area Under a Graph Long Questions (Question 1 & 2)

Question 1:

The diagram above shows the distance-time graph of a moving particle for 5 seconds. Find
(a) the distance travel by the particle from the time 2 second to 5 second.
(b)   the speed of the particle for the first 2 seconds.

Solution:

(a)
Distance travel by the particle from the time 2 second to 5 second
= 20 – 15
= 5 m

(b)
The speed of the particle for the first 2 seconds
$\begin{array}{l}=\frac{15-0}{2-0}\\ =7.5{\text{ms}}^{-1}\end{array}$

Question 2:

The diagram above shows the distance-time graph of a moving car for 12 seconds. Find
(a)    the value of v, if the average speed of the car for the first 6 seconds is
2 ms-1.
(b)   average speed of the car for the first 8 seconds.

Solution:

(a)
Average speed of the car for the first 6 seconds is 2 ms-1
$\begin{array}{l}\frac{\text{Total distance travelled}}{\text{Total time taken}}=2\\ \frac{v}{6}=2\\ v=12\end{array}$
(b)
Average speed of the car for the first 8 seconds
$\begin{array}{l}=\frac{15}{8}\\ =1.875\text{}m{s}^{-1}\end{array}$