09 3.2 Instantaneous and average velocity
- In real journeys a car does not keep a fixed velocity: it speeds up, slows down, or stops at lights.
- To describe such motion we use two quantities.
Instantaneous velocity (v)
- — the velocity of the body at a certain moment.
- It can be read from the speedometer at that moment (as a speed).
- On a displacement–time graph it is the slope of the tangent to the curve at the point corresponding to that moment.
Average velocity (v̄) — the total displacement from the starting point to the end point divided by the total time:
v̄ = (final position − initial position) / total time = Δd / Δt
On a displacement–time graph it is the slope of the straight line (chord) joining the starting point and the end point.
Example 1 — average velocity of a two-part trip. A bus travels 120 km east in 1.5 h and then 60 km east in 0.5 h. Total displacement = 180 km; total time = 2.0 h. v̄ = 180/2 = 90 km/h east. (This is neither 80 km/h nor 120 km/h: do not average the two part-velocities, 80 and 120, unless the times are equal.)
Example 2 — return trip. A student walks 600 m east in 5 min and then 600 m back west in 5 min.
- Displacement = 0 → average velocity = 0.
- Distance = 1200 m, so average speed = 1200/600 s = 2 m/s. This shows that speed and velocity are different quantities.
Example 3 — how long? A car moves with an average velocity of 15 m/s. How long does it take to cover 4.5 km? t = 4500/15 = 300 s = 5 min.