Average Speed and Average Velocity
Over elapsed time Delta t, average speed equals total distance/Delta t and average velocity equals Delta x/Delta t. For equal distances the relevant mean of speeds is harmonic, not arithmetic.
Why this shows up in the exam
Multi-leg journeys · Round trips · Mixed equal-time and equal-distance travel
Learn the idea
Average speed uses total distance, whereas average velocity uses net displacement. A round trip has a positive average speed because ground was covered, but its average velocity can be zero because the endpoint is the starting point. Unequal segments must be weighted by their actual times.
🧠 Memory hook: Average means total over total; first decide distance or displacement.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v_avg = Delta x/Delta t — signed average velocity
- speed_avg = total distance/Delta t — average rate of path accumulation
- speed_avg = 2v1v2/(v1+v2) — two equal-distance legs with constant speeds v1 and v2
How to approach it
- 1Build a distance-time table
- 2Find each leg time
- 3Divide the requested total numerator by total time
Common slip-ups that cost marks
- •Averaging speeds without time weights
- •Using displacement when average speed is asked
- •Using the equal-distance formula for equal-time intervals
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
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