Relative Motion in 1D — IISER Physics MCQs with Solutions
Free IISER Physics Relative Motion in 1D MCQs with step-by-step solutions (25 questions). Part of Relative Motion (1D and 2D). Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Relative Motion in 1D · easy · theory
The velocity of a body A relative to a body B is defined as:
A. $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$ ✓ Correct
B. $\vec{v}_{AB} = \vec{v}_A \times \vec{v}_B$
C. $\vec{v}_{AB} = \vec{v}_A + \vec{v}_B$
D. $\vec{v}_{AB} = \vec{v}_B - \vec{v}_A$
Solution: Core equation: v⃗_AB = v⃗_A − v⃗_B — the velocity of A as measured in the frame of B.
Q2 — Relative Motion in 1D · easy · theory
Two cars move in the SAME direction with speeds v_A and v_B (v_A > v_B). The magnitude of the relative velocity of A with respect to B is:
A. v_A
B. zero
C. v_A + v_B
D. v_A − v_B ✓ Correct
Solution: Same direction ⇒ magnitudes subtract: |v_AB| = v_A − v_B. Speed-trick: same direction → subtract; opposite → add.
Q3 — Relative Motion in 1D · easy · theory
Two trains approach each other with speeds v₁ and v₂. The relative speed of one with respect to the other is:
A. v₁ + v₂ ✓ Correct
B. √(v₁² + v₂²)
C. zero
D. v₁ − v₂
Solution: Opposite directions ⇒ relative speed = v₁ + v₂ (they close the gap at the sum of speeds).
Q4 — Relative Motion in 1D · easy · theory
The relative velocity of A with respect to B and the relative velocity of B with respect to A are:
A. Unrelated to each other
B. Equal in magnitude but opposite in direction ✓ Correct
C. Equal in magnitude and direction
D. Always zero
Solution: v⃗_AB = −v⃗_BA. They have the same magnitude and opposite directions.
Q5 — Relative Motion in 1D · easy · theory
Two bodies moving with equal velocities (same speed and direction) have a relative velocity of:
A. Infinite
B. Equal to their common speed
C. Twice the common speed
D. Zero — each appears at rest to the other ✓ Correct
Solution: v⃗_AB = v⃗_A − v⃗_B = 0; each body appears stationary in the other's frame (like two parallel trains at equal speed).
Q6 — Relative Motion in 1D · medium · theory
Two stones are dropped from the same height, one 1 s after the other. During their fall (both in air), the relative velocity between them:
A. Becomes zero
B. Increases with time
C. Decreases with time
D. Remains constant ✓ Correct
Solution: Both have the same acceleration g, so relative acceleration = 0 and the relative velocity (g × 1 s) stays constant. Speed-trick: free-falling bodies see each other move uniformly.
Q7 — Relative Motion in 1D · medium · theory
The relative acceleration between two bodies both moving freely under gravity is:
A. g upward
B. Zero ✓ Correct
C. g downward
D. 2g downward
Solution: a⃗_rel = a⃗_A − a⃗_B = g − g = 0. Relative motion between projectiles is uniform (straight-line).
Q8 — Relative Motion in 1D · medium · theory
For a faster body A to overtake a slower body B moving in the same direction, the time taken to close an initial gap d is:
A. d/(v_A − v_B) ✓ Correct
B. d/v_A
C. d/(v_A + v_B)
D. d/v_B
Solution: Overtaking (same direction): t = separation / relative speed = d/(v_A − v_B).
Q9 — Relative Motion in 1D · easy · theory
When a train passes a pole, the distance it covers (relative to the pole) equals:
A. Its own length ✓ Correct
B. The length of the platform
C. Zero
D. Twice its length
Solution: To pass a point object the train must move forward by its own length L, so t = L/v.
Q10 — Relative Motion in 1D · medium · theory
When two trains of lengths L₁ and L₂ cross each other, the distance covered relative to each other is:
A. L₁ − L₂
B. (L₁ + L₂)/2
C. L₁
D. L₁ + L₂ ✓ Correct
Solution: They must clear both lengths: relative displacement = L₁ + L₂, so t = (L₁+L₂)/v_rel.
Q11 — Relative Motion in 1D · easy · numerical
Car A moves at 60 km/h and car B at 40 km/h in the same direction. The velocity of A relative to B is:
A. 20 km/h ✓ Correct
B. 100 km/h
C. 40 km/h
D. 60 km/h
Solution: v_AB = v_A − v_B = 60 − 40 = 20 km/h (in the direction of motion).
Q12 — Relative Motion in 1D · easy · numerical
Two trains approach each other at 40 km/h and 50 km/h. Their relative speed is:
A. 45 km/h
B. 90 km/h ✓ Correct
C. 2000 km/h
D. 10 km/h
Solution: Opposite directions ⇒ v_rel = 40 + 50 = 90 km/h.
Q13 — Relative Motion in 1D · easy · numerical
A 100 m long train moving at 20 m/s crosses a pole in:
A. 10 s
B. 2 s
C. 5 s ✓ Correct
D. 20 s
Solution: t = L/v = 100/20 = 5 s.
Q14 — Relative Motion in 1D · medium · numerical
A 150 m train moving at 25 m/s crosses a 350 m long platform in:
A. 14 s
B. 20 s ✓ Correct
C. 10 s
D. 6 s
Solution: Distance = train + platform = 150 + 350 = 500 m; t = 500/25 = 20 s.
Q15 — Relative Motion in 1D · medium · numerical
Two trains, 100 m and 200 m long, move towards each other at 10 m/s and 20 m/s. The time they take to cross each other is:
A. 30 s
B. 10 s ✓ Correct
C. 15 s
D. 5 s
Solution: v_rel = 30 m/s; distance = 300 m; t = 300/30 = 10 s.
Q16 — Relative Motion in 1D · medium · numerical
Two trains, each 120 m long, move in the same direction at 30 m/s and 18 m/s. The faster train passes the slower one completely in:
A. 12 s
B. 5 s
C. 20 s ✓ Correct
D. 8 s
Solution: v_rel = 30 − 18 = 12 m/s; distance = 120 + 120 = 240 m; t = 240/12 = 20 s.
Q17 — Relative Motion in 1D · medium · numerical
A police car at 90 km/h chases a thief's car at 72 km/h, initially 500 m ahead. The police car catches it in:
A. 100 s ✓ Correct
B. 20 s
C. 250 s
D. 50 s
Solution: v_rel = 90 − 72 = 18 km/h = 5 m/s; t = 500/5 = 100 s.
Q18 — Relative Motion in 1D · easy · numerical
Two cars, 150 m apart, drive towards each other at 10 m/s and 5 m/s. They meet after:
A. 10 s ✓ Correct
B. 30 s
C. 15 s
D. 7.5 s
Solution: t = separation/relative speed = 150/(10 + 5) = 10 s.
Q19 — Relative Motion in 1D · medium · numerical
A ball is dropped from a tower. One second later another ball is dropped from the same point (g = 10 m/s²). The relative velocity between them while both fall is:
A. Zero
B. 20 m/s (constant)
C. Increasing with time
D. 10 m/s (constant) ✓ Correct
Solution: First ball is 10 m/s faster when the second is released; relative acceleration is zero, so the 10 m/s difference stays constant.
Q20 — Relative Motion in 1D · medium · numerical
A stone is thrown up at 20 m/s and simultaneously another is dropped from a point 60 m directly above (g = 10 m/s²). They meet after:
A. 2 s
B. 6 s
C. 3 s ✓ Correct
D. 1.5 s
Solution: Relative velocity of approach = 20 m/s (relative acceleration zero); t = 60/20 = 3 s. Speed-trick: with both in free fall, treat approach as uniform.
Q21 — Relative Motion in 1D · medium · numerical
A man in a train moving at 20 m/s sees another train on a parallel track moving in the same direction at 15 m/s. To him, the other train appears to move:
A. Backward at 5 m/s ✓ Correct
B. Forward at 35 m/s
C. At rest
D. Forward at 5 m/s
Solution: v_other,man = 15 − 20 = −5 m/s: the slower train appears to drift backward at 5 m/s.
Q22 — Relative Motion in 1D · medium · numerical
Car A accelerates from rest at 2 m/s² while car B beside it moves at a constant 10 m/s in the same direction. A catches up with B's velocity after:
A. 5 s ✓ Correct
B. 10 s
C. 2 s
D. 20 s
Solution: Equal speeds when 2t = 10 ⇒ t = 5 s.
Q23 — Relative Motion in 1D · medium · numerical
Two bodies start from the same point along the same line: A at constant 10 m/s and B from rest with acceleration 2 m/s². B catches A after:
A. 20 s
B. 4 s
C. 10 s ✓ Correct
D. 5 s
Solution: Equal displacements: 10t = ½(2)t² ⇒ 10t = t² ⇒ t = 10 s.
Q24 — Relative Motion in 1D · medium · numerical
A 200 m train overtakes a man walking at 2 m/s in the same direction, in 10 s. The speed of the train is:
A. 18 m/s
B. 22 m/s ✓ Correct
C. 20 m/s
D. 24 m/s
Solution: Relative speed = 200/10 = 20 m/s; v_train = 20 + 2 = 22 m/s (same direction, so add back the man's speed).
Q25 — Relative Motion in 1D · medium · numerical
Two cars, 100 km apart, drive towards each other at 40 km/h and 60 km/h. The distance travelled by the faster car before they meet is:
A. 100 km
B. 40 km
C. 50 km
D. 60 km ✓ Correct
Solution: They meet after t = 100/100 = 1 h; the faster car covers 60 × 1 = 60 km.