Speed and Velocity
Instantaneous velocity is the signed rate v = dx/dt, while instantaneous speed is |v|. In one dimension the sign of v identifies motion along or opposite the positive axis.
Why this shows up in the exam
Reading motion direction · Converting position laws to velocity · Distinguishing speed-time from velocity-time plots
Learn the idea
Speed tells how fast; velocity also carries the chosen one-dimensional direction. A speedometer cannot tell whether a car is moving left or right. Velocity adds that directional sign, so two equal speeds can correspond to opposite velocities.
🧠 Memory hook: Velocity has a sign; speed has only size.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = dx/dt — instantaneous signed velocity
- speed = |v| — non-negative magnitude of velocity
How to approach it
- 1Declare the positive direction
- 2Differentiate position if needed
- 3Use the sign for direction and magnitude for speed
Common slip-ups that cost marks
- •Calling a negative velocity a negative speed
- •Ignoring the chosen positive axis
- •Assuming constant speed always means constant velocity outside straight-line motion
🌟 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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