Average velocity and average speed
Average velocity is displacement over time; compute it piecewise when speed changes.
In this lesson
- Average velocity is displacement over time; compute it piecewise when speed changes.
Half the time at 40 km/h, half at 60 km/h: the average is 50. Half the DISTANCE at each: it is not!
Average velocity = total displacement ÷ total time. Average speed = total distance ÷ total time. When segments are defined by time, time-weight the speeds; when defined by distance, distance-weight the times (harmonic-style average).
For equal distances at speeds v₁ and v₂: average speed = 2v₁v₂/(v₁+v₂). Memorise it, and know why.
Average speed for two equal-distance legs
Worked example
The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.
- Area under the a–t graph = change in velocity.
- Area = 2 m/s² × 4 s = 8 m/s (the last 2 s add nothing).
Answer: 8
Transcript (0 min)
WEBVTT 1 00:00:00.000 --> 00:00:05.000 Average velocity and average speed — FemtoLearn. 2 00:00:05.000 --> 00:00:15.000 Average velocity is displacement over time; compute it piecewise when speed changes.
Frequently asked
Why is the equal-distance average not the arithmetic mean?
Time spent at each speed differs; the harmonic mean weights by time.
Practice
Free · 4 questions with full solutions- Q1 · Numerical · difficulty 2/5
The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.
- Q2 · MCQ · difficulty 2/5
A particle moves with constant velocity. Which a–t graph describes it?
- A horizontal line at a = 0
- A horizontal line at a = 2 m/s²
- A straight line through the origin
- A parabola
- Q3 · Numerical · difficulty 2/5
A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.
- Q4 · MCQ · difficulty 2/5
The slope of a velocity–time graph gives:
- Displacement
- Acceleration
- Speed
- Distance