Relative Velocity and Motion Analysis
Explore how to determine the velocity of one object relative to another and analyze motion from different reference frames, including periodic motion.
Why this shows up in the exam
NEET often asks you to solve problems involving moving observers or objects, testing your grasp of relative motion.
How NEET tests this
Learn the idea
Relative velocity is the velocity of one object as seen from another, obtained by vector subtraction v_AB = v_A – v_B. When two motions are in the same direction, the speed of the combined motion (ground speed) is the algebraic sum of the individual speeds, which lets you convert given times into speeds and back.
🧠 Memory hook: Same direction → add speeds for ground motion; opposite direction → add for relative speed, subtract for same‑direction relative speed
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Relative velocity of A w.r.t B: v_AB = v_A – v_B (vector subtraction)
- If A and B move in the same straight line, the magnitude of v_AB = |v_A – v_B| (difference of speeds)
- If A and B move in opposite directions, the magnitude of v_AB = v_A + v_B (sum of speeds)
- Speed = distance ÷ time; therefore distance = speed × time
- When two bodies move together in the same direction, the ground speed of the body that walks on a moving platform is v_walk + v_platform
How to approach it
- 1Write the length of the escalator as L (common distance)
- 2Express Preeti’s walking speed as v_p = L/t₁ and escalator speed as v_e = L/t₂
- 3Since both move upward, the speed relative to ground is v_p + v_e; compute the combined speed
- 4Time on moving escalator = L ÷ (v_p + v_e) and simplify to t₁t₂/(t₁+t₂)
Worked example — watch it click
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk up on the moving escalator will be:
- A)t₁+t₂/2
- B)t₁t₂/t₁-t₂
- ✅t₁t₂/t₁+t₂
- D)t₁-t₂
The concept behind this problem
The worked example converts the given times into individual speeds, adds the two upward speeds to get the effective speed on the moving escalator, and then uses distance = speed × time to find the required time.
Step by step
- 1Let escalator length = L.
- 2Preeti's walking speed = vₚ = L/t₁.
- 3Escalator speed = vₑ = L/t₂.
- 4When both move together, relative speed = vₚ + vₑ = L/t₁ + L/t₂ = L(t₁+t₂)/(t₁t₂).
- 5Time taken = L/(vₚ+vₑ) = L/[L(t₁+t₂)/(t₁t₂)] = t₁t₂/(t₁+t₂).
Watch out
A common mistake is to place (t₁‑t₂) in the denominator, confusing subtraction of speeds with addition of speeds for the combined motion.
Common slip-ups that cost marks
- •Do not treat “same‑direction” as a case for adding speeds in the relative‑velocity formula; the addition applies to the resultant ground speed, not to v_AB
- •Never forget to keep the same distance L for all three situations; mixing different distances gives wrong algebra
- •Watch the sign when subtracting – using t₁‑t₂ instead of t₁+ t₂ flips the answer
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk up on the moving escalator will be:
Push further
More challenging2 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.
A person walks on a moving walkway. If the person walks in the direction of the walkway's motion, they cover a distance 'L' in 20 seconds. If the person walks against the direction of the walkway's motion, they cover the same distance 'L' in 60 seconds. Assuming the person's speed relative to the walkway is constant, and the walkway's speed is also constant, what is the time taken for the person to cover distance 'L' if the walkway is stationary?
More from Kinematics
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Equations of Motion and Uniform Acceleration
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Projectile Motion
Study the motion of projectiles, including the independence of horizontal and vertical components, trajectory equations, maximum height, and the effect of initial conditions.
Position, Path Length, and Displacement
For one-dimensional motion, displacement over an interval is Delta x = x_f - x_i and may be positive, negative, or zero. Distance is the non-negative path length, so distance is always at least |Delta x|.
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.
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.