Graphs 3

3 marks · Normal

The distance–time graph for a motorbike shows the following points: at 0 minutes, 0 km; at 15 minutes, 18 km; at 20 minutes, 18 km; at 40 minutes, 54 km.

a) Calculate the speed of the motorbike during the first 15 minutes.

b) Explain what the graph shows between 15 and 20 minutes.

c) Calculate the average speed for the whole journey.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 72 km/h

(b) The bike is stationary (not moving).

Common mistakes: Not converting minutes to hours; Incorrect interpretation of stationary period

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Correctly calculates speed as distance/time for first 15 min and converts to hours.

B1 · 1 mark · States bike is stationary or not moving between 15 and 20 minutes.

M1 · 1 mark · Correctly adds total distance and divides by total time (in hours) for average speed.

Worked solution

a) 0-15 min: distance = 18 km, time = 15 min = 0.25 h; speed = 18/0.25 = 72 km/h

b) Distance remains the same: the bike is stationary for 5 minutes.

c) Total distance: 54 km; total time: 40 min = 0.6667 h; average speed = 54/0.6667 ≈ 81 km/h.