Finally, to understand the relative nature of motion, we introduce the concept of relative velocity.
-- NCERT Class 11 Physics, Ch. 2, p. 13Relative Velocity
8 MCQs1 revision card9-step worked example
Source: NCERT KinematicsPYQ coverage: NEET 2025Official key: NTA-verifiedLast updated: 7 Oct 2026
Try this first
Which expression gives the velocity of object 1 relative to object 2?
- A.v1 + v2
- B.v1 - v2
- C.v2 - v1
- D.v1 x v2
Tap to see the answer
Answer: B. B is correct: NCERT gives the velocity of object 1 relative to object 2 as v12 = v1 - v2 (NCERT Class 11 Physics, Chapter 3, page 46).
A is wrong: A is wrong because v1 + v2 is the resultant velocity of an object subjected to two velocities, which NCERT tells you to distinguish from the relative velocity.
C is wrong: C is wrong because v2 - v1 is the velocity of object 2 relative to object 1, the opposite of what is asked.
D is wrong: D is wrong because a product of two velocities is not a velocity; relative velocity is a vector difference.
Relative Velocity, explained for NEET
The trap is the direction. Relative velocity is a vector difference, so two bodies on one line give a small relative speed when they move the same way and a large one when they move opposite ways. Treating both cases with the same arithmetic is the usual lost mark.
NCERT introduces relative velocity in Chapter 2 to explain the relative nature of motion (NCERT Class 11 Physics, Chapter 2, page 13). The one place where the 2026 books state the rule is in Points to Ponder in Chapter 3: an object subjected to two velocities v1 and v2 has a resultant velocity v = v1 + v2, which must not be confused with the velocity of object 1 relative to object 2, v12 = v1 - v2, where v1 and v2 are velocities with reference to some common reference frame (NCERT Class 11 Physics, Chapter 3, page 46). The 2026 reprint lists a section on relative velocity in its contents but gives no worked treatment, so everything below the formula is derived from that one line.
On a straight line, choose a positive direction first (NCERT Class 11 Physics, Chapter 2, page 21: position to the right of the origin is positive, to the left negative). Give each velocity its sign, then subtract. Same direction: v12 = v1 - v2, so the relative speed is |v1 - v2|. Opposite directions: the signs differ, so the relative speed is |v1| + |v2|.
The NEET shape is the bus problem. Buses leave both ends of a route every T minutes, each at speed v, a distance L apart. An observer moving at speed u meets a bus after L / (v - u) in the same direction and after L / (v + u) in the opposite direction. Two passing times give two equations; solve for v, then L, then T = L / v.
Watch-out: write the signed velocities before subtracting, and check the order. The velocity of 2 relative to 1 is the negative of the velocity of 1 relative to 2.
How do you solve a Relative Velocity question? A worked example
- 1
Given
A cyclist moves at 20 km/h along a route served by buses of equal speed that leave both ends at equal intervals T. A bus overtakes the cyclist every 30 min in the direction of the ride and a bus meets the cyclist every 10 min in the opposite direction.
- 2
Required
The speed v of the buses and the interval T between buses.
- 3
Concept
The speed of a bus relative to the cyclist is v - 20 km/h in the same direction and v + 20 km/h in the opposite direction (NCERT Class 11 Physics, Chapter 3, page 46). The gap L between successive buses is the same in both cases.
- 4
Formula
L = (v - u) t1 = (v + u) t2, and T = L / v.
- 5
Substitution
(v - 20)(0.5 h) = (v + 20)(1/6 h).
- 6
Calculation
Multiplying by 6: 3(v - 20) = v + 20, so 3v - 60 = v + 20 and v = 40 km/h. Then L = (40 - 20)(0.5) = 10 km and T = L / v = 10 / 40 h = 0.25 h = 15 min. The factors 3 and 6 are exact and do not affect the significant figures.
- 7
Final answer
The buses travel at 40 km/h and leave every 15 min.
- 8
Common trap
Using v - u for both cases, or v + u for both. The same-direction case has the smaller relative speed and the longer passing time, which is why 30 min goes with v - u and 10 min with v + u.
- 9
Similar NEET-style question
A walker at 5 km/h is overtaken by a bus every 30 min in the direction of walking and meets a bus every 10 min in the opposite direction. Find the speed of the buses and the interval between them. (Answer: (v - 5)(0.5) = (v + 5)(1/6), so 3v - 15 = v + 5 and v = 10 km/h; L = (10 - 5)(0.5) = 2.5 km and T = L / v = 2.5 / 10 h = 15 min.)
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Can you answer these Relative Velocity MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
Which expression gives the velocity of object 1 relative to object 2?
Show answer and why every option is right or wrong
Answer: B. B is correct: NCERT gives the velocity of object 1 relative to object 2 as v12 = v1 - v2 (NCERT Class 11 Physics, Chapter 3, page 46).
Why A is wrong: A is wrong because v1 + v2 is the resultant velocity of an object subjected to two velocities, which NCERT tells you to distinguish from the relative velocity.
Why C is wrong: C is wrong because v2 - v1 is the velocity of object 2 relative to object 1, the opposite of what is asked.
Why D is wrong: D is wrong because a product of two velocities is not a velocity; relative velocity is a vector difference.
MCQ 2Easy RecallPractice
For the relation v12 = v1 - v2 to hold, in which frame must v1 and v2 be measured?
Show answer and why every option is right or wrong
Answer: D. D is correct: NCERT states that v1 and v2 are velocities with reference to some common reference frame (NCERT Class 11 Physics, Chapter 3, page 46).
Why A is wrong: A is wrong because in its own rest frame each object has zero velocity, so no difference could be formed.
Why B is wrong: B is wrong because subtracting velocities measured in different frames gives a number with no physical meaning.
Why C is wrong: C is wrong because mixing frames for the two objects breaks the subtraction; one common frame must be used.
MCQ 3Easy RecallPractice
NCERT introduces the concept of relative velocity in Chapter 2 in order to understand which feature of motion?
Show answer and why every option is right or wrong
Answer: A. A is correct: the chapter introduction says that, to understand the relative nature of motion, the concept of relative velocity is introduced (NCERT Class 11 Physics, Chapter 2, page 13).
Why B is wrong: B is wrong because the chapter treats kinematics only; friction is not part of the reason given for relative velocity.
Why C is wrong: C is wrong because path curvature belongs to motion in a plane, not to the reason given for relative velocity.
Why D is wrong: D is wrong because variation of g with height is a gravitation topic and is not mentioned in this connection.
MCQ 4Direct ApplicationPractice
Two cars move on a straight road in the same direction, one at 72 km/h and the other at 54 km/h. What is the speed of the faster car relative to the slower car?
Show answer and why every option is right or wrong
Answer: C. C is correct: same direction, so v12 = v1 - v2 = 72 - 54 = 18 km/h (NCERT Class 11 Physics, Chapter 3, page 46).
Why A is wrong: A is wrong because 126 km/h adds the speeds, which is the result for opposite directions, not the same direction.
Why B is wrong: B is wrong because 36 km/h is half of the faster speed, which is not a relative speed.
Why D is wrong: D is wrong because 9 km/h is half of the correct difference.
MCQ 5Direct ApplicationPractice
A train A moves east at 40 m/s and a train B moves west at 30 m/s on parallel tracks. What is the speed of A relative to B?
Show answer and why every option is right or wrong
Answer: C. C is correct: take east as positive, so v1 = +40 m/s and v2 = -30 m/s, and v12 = 40 - (-30) = 70 m/s (NCERT Class 11 Physics, Chapter 3, page 46).
Why A is wrong: A is wrong because 10 m/s is the difference of the speeds, which applies when both trains move in the same direction.
Why B is wrong: B is wrong because 35 m/s is the average of the speeds, which is not a relative speed.
Why D is wrong: D is wrong because 1.3 is the ratio 40 / 30, which has no unit of speed.
MCQ 6Direct ApplicationPractice
Take east as positive. Car A has velocity +25 m/s and car B has velocity -15 m/s. What is the velocity of B relative to A?
Show answer and why every option is right or wrong
Answer: A. A is correct: v(B relative to A) = vB - vA = -15 - 25 = -40 m/s, so B appears to move west at 40 m/s from A (NCERT Class 11 Physics, Chapter 3, page 46, with east taken as positive as in Chapter 2, page 21).
Why B is wrong: B is wrong because +40 m/s is the velocity of A relative to B; the order of subtraction is reversed.
Why C is wrong: C is wrong because -10 m/s adds the signed velocities instead of subtracting them.
Why D is wrong: D is wrong because +10 m/s adds the signed velocities and loses the sign of B's motion.
MCQ 7CalculationPractice
A cyclist rides at 15 km/h along a route on which buses of equal speed leave both ends at equal intervals. A bus overtakes the cyclist every 36 min in the direction of the ride, and a bus passes the cyclist every 12 min in the opposite direction. What are the interval T between buses and the speed of the buses?
Show answer and why every option is right or wrong
Answer: D. D is correct: the gap L between buses satisfies L = (v - 15)(0.6 h) = (v + 15)(0.2 h), so 3v - 45 = v + 15 and v = 30 km/h. Then L = 15 x 0.6 = 9 km and T = L / v = 9 / 30 h = 18 min (NCERT Class 11 Physics, Chapter 3, page 46).
Why A is wrong: A is wrong because with v = 45 km/h and T = 24 min the gap is 18 km, giving 36 min in the same direction but 18 min, not 12 min, in the opposite direction.
Why B is wrong: B is wrong because with v = 30 km/h and T = 12 min the gap is 6 km, giving 24 min in the same direction, not 36 min.
Why C is wrong: C is wrong because with v = 60 km/h and T = 18 min the gap is 18 km, giving 24 min in the same direction, not 36 min.
MCQ 8CalculationPractice
Car A moves at 30 m/s and car B, 100 m ahead of it on the same straight road, moves in the same direction at 20 m/s. How long does A take to catch up with B?
Show answer and why every option is right or wrong
Answer: B. B is correct: the speed of A relative to B is 30 - 20 = 10 m/s, so the 100 m gap closes in 100 / 10 = 10 s (NCERT Class 11 Physics, Chapter 3, page 46).
Why A is wrong: A is wrong because 100 / (30 + 20) = 2.0 s uses the sum of the speeds, which is the opposite-direction rule.
Why C is wrong: C is wrong because 100 / 30 = 3.3 s uses only the speed of A and ignores that B is also moving.
Why D is wrong: D is wrong because 100 / 20 = 5.0 s uses only the speed of B.
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Relative Velocity: quick recall before you leave
1 card
What to remember before solving Relative Velocity questions
3 NCERT lines
An object is said to be in motion if its position changes with time. The position of the object can be specified with reference to a conveniently chosen origin. For motion in a straight line, position to the right of the origin is taken as positive and to the left as negative.
-- NCERT Class 11 Physics, Ch. 2, p. 21An object subjected to two velocities v1 and v2 has a resultant velocity v = v1 + v2. Take care to distinguish it from velocity of object 1 relative to velocity of object 2 : v12= v1 − v2. Here v1 and v2 are velocities with reference to some common reference frame.
-- NCERT Class 11 Physics, Ch. 3, p. 46Where do students lose marks on Relative Velocity?
1 trap or mistake
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Category: Sign Convention
Student fails to distinguish between same-direction and opposite-direction relative velocities, treating both as magnitudes.
When it triggers
Question describes two objects moving on the same line; observer somewhere between or alongside.
How to avoid
Relative velocity is a VECTOR. Same direction: v_rel = v_a - v_b (smaller magnitude). Opposite direction: v_rel = v_a + v_b (larger magnitude). Use sign convention consistently along chosen axis.
Relative Velocity: NEET previous year questions (PYQs) with answers
1 question from NEET 2025, answers verified against NTA official keys
NEET 2025
115 min, 120 km/h
29 min, 40 km/h
325 min, 100 km/h
410 min, 90 km/h
NTA Answer: Option 1(final)
How does NEET ask about Relative Velocity?
1 recurring pattern from past papers
Buses leave both ends of a route every T minutes; observer travels between them at constant speed; given separate periods at which buses pass observer in same and opposite directions, find bus speed or T. Use relative-velocity equations: same direction T_same = L / (v_bus - v_obs), opposite T_opp = L / (v_bus + v_obs).
Multi StepMedium
Common distractors
ignores direction relative to observer
Treating bus-passing time as absolute
More in Kinematics: 15 exam traps and mistakes · 7 formulas · 9 question patterns from its other lessons.
Sources
NCERT refs: Class 11 Physics Chapter 2, p.13 | Class 11 Physics Chapter 3, p.46 | Class 11 Physics Chapter 2, p.21
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
Every past-paper question from this chapter:
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