A cyclist rides 300 m north, then 100 m south. Which pair states the distance traveled and the displacement?
In earlier grades you saw average speed: distance divided by time. And you've just seen average velocity: displacement divided by time. Same journey, two different divisions.
Average speed divides the DISTANCE, the length of the whole path, by the time. It ignores direction.
Average velocity divides the DISPLACEMENT, how far and which way the finish lies from the start, by the time. It keeps direction.
Take a delivery van that drives 60 m east, then 20 m west, in 40 s. The two divisions work on different numbers, and they give different answers.
A skater glides 60 m east, then 30 m west, in 30 s. Which pair gives her average speed and her average velocity?
A bee flies 40 m east, then 20 m west, in 20 s. What are its average speed and its average velocity?
Write down the values in the question:
legs: 40 m east, then 20 m west
time: 20 s
Average speed divides the distance, the length of the whole path:
distance = 40 + 20 = 60
average speed = 60 / 20 = 3
Average velocity divides the displacement, the finish relative to the start:
displacement = 40 − 20 = 20, east
average velocity = 20 / 20 = 1
average speed = 3 m/s; average velocity = 1 m/s east
A boat sails 300 m out to a buoy and 300 m straight back in 200 s. What are its average speed and its average velocity?
Write down the values in the question:
legs: 300 m out, then 300 m straight back
time: 200 s
Average speed divides the distance:
distance = 300 + 300 = 600
average speed = 600 / 200 = 3
Average velocity divides the displacement:
The boat finishes where it started, so its displacement is 0 m.
average velocity = 0 / 200 = 0
average speed = 3 m/s; average velocity = 0 m/s
The round trip is the extreme case. You met it on the 400 m track: one lap in 100 s is an average speed of 4 m/s, and a displacement of 0 m, so an average velocity of 0 m/s. Plenty of ground covered; overall, nowhere.
A dog runs 30 m out along a straight beach path and 30 m straight back, taking 20 s. Which pair gives its average speed and its average velocity?
At the other extreme, a journey that never bends or doubles back has a path exactly as long as its displacement's size, so the two averages come out equal in size.
For which journey do the average speed and the size of the average velocity come out equal?
A bus drives its 600 m loop route in 200 s, ending at the depot where it started. What are its average speed and its average velocity?
A hiker walks 120 m north, then 40 m south, taking 40 s in total. What are her average speed and her average velocity?
Can a journey's average velocity ever be larger in size than its average speed?