The graph represents the motion of a vehicle during part of a journey. What is the best estimate of the distance travelled during the part of the journey shown?

Answer:

15) D

We know that total distance travelled = area under graph. 

However, remember to always convert the minutes into seconds as the speed is given in metres/second

Let us split the graph into a trapezium, a rectangle and a triangle. 

Area under trapezium = [h (a+b)] ÷ 2

[60 seconds (15+20)] ÷ 2 = (60 x 35) ÷ 2 = 30 x 35 = 1050m

Area under rectangle = (240 – 60) x 20 = 180 x 20 = 3600 m

Area under triangle = ½ b x h = ½ x 180 x 20 = 1800 m

Total distance = 1050 + 3600 + 1800 = 6450 m = 6.45 km

However, you must remember that the triangle is not really a triangle as one side is curved. Since it is curved towards the x-axis, the area will actually be smaller than the one we obtained. 

Hence distance =  < 6.45 km

The answer is 6.00 km. Option D.