The difference between speed and velocity
5 marks · HardA hiker takes a trip starting at point X, walking 2.0 km east to point Y, then 1.5 km north to point Z, all in a total time of 45 minutes.
Calculate the hiker’s average speed for the journey. Give your answer in km/h.
Calculate the hiker’s average velocity for the journey. Give your answer as a magnitude in km/h and a compass direction from X to Z (to the nearest degree).
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) 4.67 km/h
(b) 2.54 km/h, direction 37° north of east
Common mistakes: Using displacement instead of total distance for speed; not converting minutes to hours; forgetting to use Pythagoras for displacement; giving answer as only magnitude for velocity; giving direction as relative to north or east incorrectly.
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly calculates and sums the total distance (2.0 km + 1.5 km).
A1 (a) · 1 mark · Divides total distance by total time in hours and gives correct units. (follow-through)
M1 (b) · 1 mark · Calculates straight-line displacement using Pythagoras' theorem.
A1 (b) · 1 mark · Divides displacement by total time for magnitude of velocity, gives correct value and unit. (follow-through)
B1 (b) · 1 mark · Correctly calculates the angle of direction from east or north and expresses as, e.g., '37° north of east'.
Worked solution
a) Average speed = total distance / total time
b) Displacement is the straight line from X to Z:
So the direction is 37° north of east. The final answer: average velocity = 3.33 km/h, 37° north of east.