Motion in a Straight Line – Relative Motion in One Dimension: NEET MCQs with Answers

14 free questions on Motion in a Straight Line – Relative Motion in One Dimension for NEET (UG), starting with previous-year NEET and AIPMT questions. Try each one, then tap Show answer for the answer and a short explanation.

Syllabus covered: Relative Motion in One Dimension

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Question 1

Previous-year question
The speed of a swimmer in still water is 20 m/s. The speed of the river water is 10 m/s and it is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to north is given by [NEET 2019]
  1. 30° west
  2. 0°
  3. 60° west
  4. 45° west
Show answer
Answer: (A) 30° west
Explanation: For the shortest path the swimmer must head upstream at an angle θ such that his upstream component cancels the current: sin θ = 10/20 = ½. Hence θ = 30° west of north.

Question 2

Previous-year question
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 [NEET 2017]
  1. t₁t₂/(t₂ − t₁)
  2. t₁t₂/(t₂ + t₁)
  3. t₁ − t₂
  4. (t₁ + t₂)/2
Show answer
Answer: (B) t₁t₂/(t₂ + t₁)
Explanation: Taking the escalator length as L, her walking speed is L/t₁ and the escalator's speed is L/t₂. On the moving escalator these add, giving L/t₁ + L/t₂, so the time = L divided by this = t₁t₂/(t₁ + t₂).

Question 3

Previous-year question
A train of 150 m length is going towards the North direction at a speed of 10 m/s. A parrot flies at a speed of 5 m/s towards the South direction, parallel to the railway track. The time taken by the parrot to cross the train is [AIPMT 1992]
  1. 12 s
  2. 8 s
  3. 15 s
  4. 10 s
Show answer
Answer: (D) 10 s
Explanation: The parrot and the train travel in opposite directions, so their relative speed is the sum of the individual speeds. Taking North as positive, v_train = +10 m/s and v_parrot = −5 m/s: v_rel = |v_parrot − v_train| = |−5 − 10| = 15 m/s To cross the train, the parrot must cover the full length of the train relative to it: t = length/relative speed = 150/15 = 10 s. The length of the parrot is neglected, and the answer does not depend on the ground frame at all — only on the relative motion.

Question 4

Previous-year question
A bus is moving with a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km ahead of the scooterist, with what speed should the scooterist chase the bus? [AIPMT 2009]
  1. 20 ms⁻¹
  2. 40 ms⁻¹
  3. 25 ms⁻¹
  4. 10 ms⁻¹
Show answer
Answer: (A) 20 ms⁻¹
Explanation: To overtake, the scooterist must close the 1 km gap. Working in the frame of the bus, the relative displacement required is 1000 m in 100 s, so the relative velocity must be v_rel = 1000/100 = 10 ms⁻¹ Since both vehicles move along the same direction, the relative velocity of the scooter with respect to the bus is v_rel = v_S − v_B Therefore v_S = v_rel + v_B = 10 + 10 = 20 ms⁻¹.

Question 5

Previous-year question
Preeti walks up a stationary escalator in time t₁. If she stands stationary on the moving escalator it takes her up in time t₂. The time taken by her to walk up the moving escalator is [NEET 2017]
  1. (t₁ + t₂)/(t₂ − t₁)
  2. t₁ t₂/(t₂ + t₁)
  3. t₁ − t₂
  4. (t₁ + t₂)/2
Show answer
Answer: (B) t₁ t₂/(t₂ + t₁)
Explanation: Rates add: 1/t = 1/t₁ + 1/t₂ ⇒ t = t₁ t₂/(t₁ + t₂).

Question 6

Previous-year question
A bus moves at 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is 1 km ahead, the scooterist's required speed is [AIPMT 2009]
  1. 10 m/s
  2. 20 m/s
  3. 40 m/s
  4. 25 m/s
Show answer
Answer: (B) 20 m/s
Explanation: v×100 = 1000 + 10×100 = 2000 ⇒ v = 20 m/s.

Question 7

Ball P is thrown vertically upward from the ground at 15 m/s. At the same instant ball Q is released from rest at a height of 40 m directly above P. Until they meet, the speed of P relative to Q
  1. is (15 − 10t) m/s
  2. is (15 + 10t) m/s
  3. is zero
  4. stays 15 m/s throughout
Show answer
Answer: (D) stays 15 m/s throughout
Explanation: Both balls have the same acceleration g downward, so their relative acceleration is zero. The relative velocity therefore keeps its initial value, 15 m/s − 0 = 15 m/s upward, until they meet after 40/15 s.
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Question 8

Two cars 1.5 km apart drive towards each other along a straight road at 10 m/s and 15 m/s. A bird flying at 30 m/s starts from one car, flies to the other, turns back at once, and keeps flying to and fro until the cars meet. What total distance does the bird fly?
  1. 1500 m
  2. 900 m
  3. 1800 m
  4. 3600 m
Show answer
Answer: (C) 1800 m
Explanation: The cars approach each other at 10 + 15 = 25 m/s, so they meet after 1500/25 = 60 s. The bird flies at a constant 30 m/s for this whole time, covering 30 × 60 = 1800 m.

Question 9

A car moves along a straight road with speed v. What is the velocity of the car relative to itself?
  1. −v
  2. Zero
  3. 2v
  4. v
Show answer
Answer: (B) Zero
Explanation: The relative velocity of A with respect to B is vA − vB. When A and B are the same body, this is v − v = 0.

Question 10

A lift is moving upward with a constant upward acceleration a. A man inside the lift lets go of a ball from his hand. The magnitudes of the acceleration of the ball as measured by the man in the lift and by a person standing on the ground are respectively
  1. g + a and g
  2. g − a and g
  3. g and g + a
  4. g and g
Show answer
Answer: (A) g + a and g
Explanation: Once released, the ball falls freely, so relative to the ground its acceleration is g downward. The lift accelerates upward at a, so the acceleration of the ball relative to the lift is g − (−a) = g + a, directed downward.

Question 11

Two trains on parallel straight tracks move towards each other at 15 m/s and 25 m/s. When they are 1.2 km apart, a bird starts flying back and forth between their fronts at a constant speed of 30 m/s, turning instantly each time it reaches a train. What total distance does the bird fly before the fronts of the trains meet?
  1. 900 m
  2. 1200 m
  3. 1800 m
  4. 450 m
Show answer
Answer: (A) 900 m
Explanation: The trains close the gap at 15 + 25 = 40 m/s, so they meet after 1200/40 = 30 s. The bird flies at 30 m/s for the whole of this time, covering 30 × 30 = 900 m.

Question 12

Two cyclists ride along a straight road at constant speeds. When they ride towards each other, the distance between them decreases at 10 m/s. When they ride in the same direction with the same speeds, the distance between them increases at 4 m/s. Their speeds are
  1. 6 m/s and 4 m/s
  2. 8 m/s and 2 m/s
  3. 5 m/s and 5 m/s
  4. 7 m/s and 3 m/s
Show answer
Answer: (D) 7 m/s and 3 m/s
Explanation: Moving towards each other, the relative speed is v₁ + v₂ = 10 m/s. Moving in the same direction it is v₁ − v₂ = 4 m/s. Solving, v₁ = 7 m/s and v₂ = 3 m/s.

Question 13

A car moves along a straight road at 72 km/h. The velocity of the car measured relative to the car itself is
  1. 144 km/h
  2. 72 km/h in the backward direction
  3. 72 km/h in the forward direction
  4. zero
Show answer
Answer: (D) zero
Explanation: The velocity of a body relative to another is the difference of their velocities. Relative to itself this is v⃗ − v⃗ = 0, so every body is at rest in its own frame.

Question 14

Three cars move along the same straight road with positions x_A = 10 + 4t, x_B = 30 + 4t and x_C = 60 − 6t (x in metres, t in seconds). Which statement about their position-time lines and motion is correct?
  1. The lines of A and B are not parallel, as they have different intercepts; C reaches B at t = 3 s and A at t = 5 s
  2. The lines of A and B are parallel, so their relative velocity is zero; C reaches A at t = 3 s and B at t = 5 s
  3. The lines of A and B are parallel, so their relative velocity is zero; C reaches B at t = 3 s and A at t = 5 s
  4. The lines of A and B are parallel, so their relative velocity is zero; the velocity of C relative to A is −2 m/s
Show answer
Answer: (C) The lines of A and B are parallel, so their relative velocity is zero; C reaches B at t = 3 s and A at t = 5 s
Explanation: A and B have the same slope, 4 m/s, so their lines are parallel, the gap stays 20 m and their relative velocity is zero. The different intercepts only show different starting positions. C meets B when 30 + 4t = 60 − 6t, at t = 3 s, and meets A when 10 + 4t = 60 − 6t, at t = 5 s. The velocity of C relative to A is −6 − 4 = −10 m/s.

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