Relative Velocity on a Line
In Galilean one-dimensional motion, v_A/B = v_A - v_B in a common coordinate system. Relative acceleration similarly satisfies a_A/B = a_A - a_B.
Why this shows up in the exam
Objects seen from moving vehicles · Closing and separation rates · Throws made from a moving platform
Learn the idea
The velocity of A seen from B is the signed difference v_A minus v_B. An observer moving beside you subtracts their own motion from everything they see. Same-direction speeds partly cancel; opposite-direction signed velocities increase the closing rate.
🧠 Memory hook: Seen from B means subtract B.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v_A/B = v_A - v_B — velocity of A relative to B
- a_A/B = a_A - a_B — relative acceleration in an inertial frame
How to approach it
- 1Choose one positive direction
- 2Write both signed ground velocities
- 3Subtract observer velocity and interpret the sign
Common slip-ups that cost marks
- •Adding speed magnitudes without signs
- •Reversing observer and observed object
- •Mixing velocities measured in different frames
🌟 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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