Kinematic Definitions
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Distance and speed tell you how far and how fast. Displacement and velocity tell you that too, plus which way. Average velocity is displacement divided by time, not distance divided by time.
1. Four words that sound alike
Physics splits “how far” and “how fast” into two versions each. One version ignores direction (a scalar). The other includes direction (a vector).
To give a direction a sign, pick which way is positive (say east = +). Then a negative velocity just means “moving west.” It does not mean slowing down.
2. Distance vs. displacement
A student walks 8 m east, then 3 m west.
Distance adds up every step of the path: 8 + 3 = 11 m.
Displacement only compares where you started and where you ended. With east = +: (+8) + (−3) = +5 m, or 5 m east.
If you end where you started, your displacement is zero, no matter how far you walked.
3. Average speed vs. average velocity
A runner does one 400 m lap in 80 s and finishes where she started. Average speed = 400 m ÷ 80 s = 5 m/s. Average velocity = 0 m ÷ 80 s = 0 m/s.
Instantaneous means “at one moment.” A speedometer shows instantaneous speed: how fast right now, with no direction.
4. Example, then try it
The student in the figure takes 10 s for the whole walk (8 m east, then 3 m west). Find the average speed and average velocity.
Average speed = 11 m ÷ 10 s = 1.1 m/s
Average velocity = +5 m ÷ 10 s = +0.5 m/s (0.5 m/s east)
They are different because the student turned around.
A cyclist rides 120 m east in 20 s, then turns around and rides 40 m west in 10 s. Find her average speed and average velocity for the whole trip.
Pick a positive direction: east = +.
Distance and displacement: distance = 120 + 40 = 160 m. Displacement = (+120) + (−40) = +80 m.
Total time: 20 s + 10 s = 30 s. Average speed = 160 m ÷ 30 s ≈ 5.3 m/s.
Average velocity: +80 m ÷ 30 s ≈ +2.7 m/s.
Answer: average speed ≈ 5.3 m/s; average velocity ≈ 2.7 m/s east.
5. Common mistakes
A ball is thrown straight up and caught at the same height 2 s later. What is its average velocity for the flight?
It ends where it started, so its displacement is zero, and average velocity = 0 ÷ 2 s = 0. Its average speed is not zero, because it did travel up and back down.
Ready to practice?
5 questions on Kinematic Definitions, each with a hint and an explanation for every wrong answer.