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
= Gradient 
= 150 20 =7.5  ms 1



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
Total distance travelled Total time taken =2 v 6 =2 v=12
(b)
Average speed of the car for the first 8 seconds
= 15 8 =1.875 m s 1