6.3 Gradient and Area Under a Graph, SPM Paper 2 (Long Questions)


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



Question 3:
Diagram below shows the distance-time graph for the journey of a train from one town to another for a period of 90 minutes.


(a) State the duration of time, in minutes, during which the train is stationery.
(b) Calculate the speed, in km h-1, of the train in the first 40 minutes.
(c) Find the distance, in km, travelled by the train for the last 25 minutes.

Solution:
(a) Duration the train is stationery = 65 – 40 = 25 minutes

(b) Speed of the train in the first 40 minutes = 15090 km 40 minutes = 60 km 40 60  h =90 km / h

(c) 90 – 0 = 90 km

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