A skater glides from x₀ = +3 m to x = +11 m. Enter the displacement Δx in meters, including the sign.
A kayaker ends 40 m south of her put-in after 10 s of steady paddling. How fast is that, and in which direction? You've already seen the definition: average velocity is displacement divided by elapsed time, v = Δx / Δt. Now you calculate with it, sign and direction included.
A kayaker ends 40 m south of her put-in after 10 s of steady paddling. What is her average velocity?
Write down the values in the question:
Δx = 40 m south
Δt = 10 s
Write down the equation:
v = Δx / Δt
Substitute in the values:
v = 40 / 10
Simplify:
v = 4 m/s south
When the direction is a word, the word rides along: 40 m south over 10 s gave a southward answer.
A swimmer ends 50 m north of her starting point after 100 s. What is her average velocity?
Write down the values in the question:
Δx = 50 m north
Δt = 100 s
Write down the equation:
v = Δx / Δt
Substitute in the values:
v = 50 / 100
Simplify:
v = 0.5 m/s north
A cyclist's displacement along a straight road is +64 m over 8 s. What is her average velocity, in m/s?
When the displacement is a signed number, the sign rides along through the division instead: a negative Δx gives a negative v.
A boat moves along a straight channel that takes the harbor mouth as the positive direction. Its displacement is −120 m after 60 s. What is its average velocity?
Write down the values in the question:
Δx = −120 m
Δt = 60 s
Write down the equation:
v = Δx / Δt
Substitute in the values:
v = −120 / 60
Simplify:
v = −2 m/s
Check the size of every answer against the trip. A displacement of 120 m in 60 s means about 2 m of progress each second, so an answer of size 2 m/s fits. A value like 0.5 m/s or 7200 m/s signals a division run the wrong way, or a multiplication.
The units catch the same slips. Δx / Δt gives m ÷ s, which is m/s: correct. If your units come out as m × s, you multiplied instead of dividing. If they come out as s/m, you divided the wrong way.
A cart rolls along a straight track. Its displacement is -45 m and the trip takes 9 s. What is the cart's average velocity, in m/s? Include the sign.
A car's displacement along its straight line is -84 m in 12 s. What is its average velocity, in m/s, sign included?
A cargo boat moves along a straight river. Its displacement is -105 m over 14 s. What is its average velocity, in m/s, sign included?
A robot starts at position x = +14 m on a straight rail and ends at x = -10 m, taking 4 s for the run. What is its average velocity, in m/s?
A trail runner finishes 240 m south of the trailhead after 80 s. Taking north as the positive direction, what is her average velocity, in m/s?