A bus travels from town A to town B along a straight highway of length 120 km that lies due east–west. The journey is completed in three equal distance segments as follows:
• first one-third of the distance at a constant speed of 40 km h⁻¹,
• next one-third while accelerating uniformly from 40 km h⁻¹ to 70 km h⁻¹,
• last one-third at a constant speed of 70 km h⁻¹.
Answer the following parts.
(i) Calculate the time taken in each of the three segments.
(ii) Determine the total time of travel and hence find the average speed for the entire trip from A to B.
(iii) Taking the eastward direction as positive, find the magnitude of the average velocity for the trip.
(iv) State whether the numerical value of the average speed is greater than, less than, or equal to the magnitude of the average velocity in this situation, and justify your answer.