Which two pieces of information fix a journey's displacement?
A kayaker paddles up and down a winding river for 200 s and ends 400 m downstream of her launch point. How fast did her trip carry her downstream, overall? Speed cannot answer: speed ignores which way she ended up.
In earlier grades you saw speed = distance ÷ time. Average velocity runs the same division on the displacement instead of the distance, so the direction survives the division.
That whole-trip rate, displacement divided by elapsed time, is called the average velocity. It is the one steady velocity that would cover the same displacement in the same time.
A kayaker paddles 210 m along a winding shoreline and ends 150 m east of her put-in, 50 s after starting. In v = Δx / Δt, which of the trip's numbers plays the part of Δx?
The units combine just as speed's units do: meters divided by seconds gives m/s. And because the displacement has a direction, the average velocity keeps it. The kayaker's trip: v = 400 / 200 = 2, so her trip carried her downstream at 2 m/s, downstream.
A signed displacement keeps its sign the same way: a displacement of −20 m in 4 s gives an average velocity of −5 m/s.
A shopper's trip through a mall ends 24 m west of the entrance and takes 60 s. What is the shopper's average velocity?
Write down the values in the question:
Δx = 24 m west
Δt = 60 s
Write down the equation:
v = Δx / Δt
Substitute in the values:
v = 24 / 60
Simplify:
v = 0.4 m/s west
A canoe trip's displacement points south. What direction does the trip's average velocity have?
Two bike trips each take 50 s. Trip A ends 100 m north of its start; trip B ends 100 m south of its start. How do their average velocities compare?
Write down the values in the question:
Trip A: Δx = 100 m north, Δt = 50 s
Trip B: Δx = 100 m south, Δt = 50 s
Write down the equation:
v = Δx / Δt
Substitute in the values, one trip at a time:
Trip A: v = 100 / 50 = 2
Trip B: v = 100 / 50 = 2
Trip A: v = 2 m/s north. Trip B: v = 2 m/s south. Same size, opposite directions: two different average velocities.
A hiker's trip has a displacement of 600 m north and takes 300 s. Which statement uses average velocity correctly?
Average velocity divides a displacement in meters by an elapsed time in seconds. Which unit does average velocity carry?
A student computes an 'average velocity' for a walk that loops around a park by dividing the 500 m of path walked by the 250 s the walk took. Why is the method wrong for average velocity?