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 
= 15 0 2 0 = 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

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