A hiker moves only along the north–south direction of a straight trail in three successive stages. First, she walks 3 km due north in 45 min, then 4 km due south in 60 min, and finally 1 km due north in 15 min.
(a) Define average speed and average velocity for the entire motion.
(b) Without performing any numerical calculation of the actual values, state whether the magnitude of the hiker’s average velocity for the whole trek is less than, equal to, or greater than her average speed. Give a reason based on the given data.
(c) Explain how the hiker could change the individual speeds in the three stages without altering the calculated value of her average speed for the complete journey.