Relative Motion

RM-01

Two cars move in the same direction with speeds of 60 km/h and 40 km/h. The speed of the faster car relative to the slower car is

A. 20 km/h
B. 40 km/h
C. 60 km/h
D. 100 km/h

Correct Answer: A

Trigger

Same-direction motion

Formula / Tool

Relative Velocity

Quick Execution

60 − 40

= 20 km/h

Trap: Adding speeds instead of subtracting.

RM-02

Two trains move towards each other with speeds of 50 km/h and 70 km/h. Their relative speed is

A. 20 km/h
B. 50 km/h
C. 70 km/h
D. 120 km/h

Correct Answer: D

Trigger

Opposite-direction motion

Formula / Tool

Relative Velocity

Quick Execution

50 + 70

= 120 km/h

Trap: Subtracting speeds instead of adding them.

RM-03

Two cars move side by side in the same direction, each with a speed of 80 km/h. The speed of one car relative to the other is

A. 0 km/h
B. 40 km/h
C. 80 km/h
D. 160 km/h

Correct Answer: A

Trigger

Equal-velocity recognition

Formula / Tool

Relative Velocity

Quick Execution

80 − 80

= 0

Trap: Assuming moving objects must have non-zero relative speed.

RM-04

A passenger sitting in a train moving with constant velocity throws a ball vertically upward. To the passenger, the ball appears to

A. Move along a parabola
B. Move vertically up and down
C. Move horizontally
D. Remain at rest

Correct Answer: B

Trigger

Observer frame

Formula / Tool

Frame of Reference

Quick Execution

Ball already shares the train's horizontal velocity.

Passenger observes only vertical motion.

Trap: Using the ground-frame observation.

RM-05

A man walks at 5 m/s inside a train moving at 20 m/s in the same direction. His speed relative to the ground is

A. 5 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Correct Answer: D

Trigger

Velocity composition

Formula / Tool

Relative Velocity

Quick Execution

20 + 5

= 25 m/s

Trap: Reporting only the walking speed.

RM-06

A man walks at 5 m/s inside a train moving at 20 m/s. If he walks opposite to the train's motion, his speed relative to the ground is

A. 5 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Correct Answer: B

Trigger

Opposite internal motion

Formula / Tool

Relative Velocity

Quick Execution

20 − 5

= 15 m/s

Trap: Adding speeds automatically.

RM-07

Two particles move with constant velocities of 10 m/s and 15 m/s in the same direction. Their relative acceleration is

A. 0
B. 5 m/s²
C. 10 m/s²
D. 15 m/s²

Correct Answer: A

Trigger

Relative acceleration

Formula / Tool

a_AB = a_A − a_B

Quick Execution

Both particles have zero acceleration.

Relative acceleration = 0

Trap: Using velocity difference instead of acceleration.

RM-08

Two particles have accelerations of 4 m/s² and 4 m/s² in the same direction. Their relative acceleration is

A. 0
B. 4 m/s²
C. 8 m/s²
D. Depends on velocity

Correct Answer: A

Trigger

Equal acceleration recognition

Formula / Tool

Relative Acceleration

Quick Execution

4 − 4

= 0

Trap: Adding the accelerations.

RM-09

Rain falls vertically downward. A man running horizontally observes the rain to be

A. Vertical
B. Inclined
C. Horizontal
D. Stationary

Correct Answer: B

Trigger

Observer motion

Formula / Tool

Relative Velocity

Quick Execution

Relative velocity gains a horizontal component.

Rain appears inclined.

Trap: Using the ground frame instead of the runner's frame.

RM-10

A swimmer can swim at 4 m/s in still water. The river flows at 4 m/s. If the swimmer moves directly upstream, his speed relative to the bank is

A. 0 m/s
B. 4 m/s
C. 8 m/s
D. Cannot be determined

Correct Answer: A

Trigger

Equal and opposite velocities

Formula / Tool

Relative Velocity

Quick Execution

4 − 4

= 0

Trap: Adding speeds instead of comparing directions.

RM-11

Two trains moving in the same direction take 20 s to cross each other. If their relative speed doubles, the crossing time becomes

A. 5 s
B. 10 s
C. 20 s
D. 40 s

Correct Answer: B

Trigger

Crossing interpretation

Formula / Tool

Crossing Time ∝ 1 / Relative Speed

Quick Execution

Relative speed doubles.

Time becomes half.

20/2 = 10 s

Trap: Assuming crossing time remains unchanged.

RM-12

A person standing on a platform observes two trains moving with equal speeds in opposite directions. The relative speed between the trains is

A. v
B. 2v
C. v/2
D. 0

Correct Answer: B

Trigger

Symmetric opposite motion

Formula / Tool

Relative Velocity

Quick Execution

v + v

= 2v

Trap: Using subtraction instead of addition.

RM-13

Two cars move in the same direction. The rear car is slower than the front car. The separation between them will

A. Increase
B. Decrease
C. Remain constant
D. Become zero immediately

Correct Answer: A

Trigger

Gap evolution

Formula / Tool

Relative Velocity Sign

Quick Execution

Rear car slower

Gap increases with time

Trap: Ignoring the sign of relative velocity.

RM-14

Two runners move with equal speeds in the same direction on parallel tracks. One runner can never overtake the other because

A. Relative acceleration is zero
B. Relative velocity is zero
C. Speeds are small
D. Distance is large

Correct Answer: B

Trigger

Overtaking condition

Formula / Tool

Relative Velocity

Quick Execution

Equal speeds

Relative speed = 0

Trap: Focusing on initial separation instead of relative speed.

RM-15

A train moves with constant velocity. A passenger releases a ball from hand. To a person standing on the ground, the ball follows

A. A vertical line
B. A horizontal line
C. A parabolic path
D. A circular path

Correct Answer: C

Trigger

Different observer frames

Formula / Tool

Relative Motion of a Projectile

Quick Execution

Ball retains train's horizontal velocity.

Trajectory is parabolic.

Trap: Using the passenger's frame instead of the ground frame.

RM-16

Two cars are 100 m apart and move towards each other with speeds of 10 m/s and 15 m/s. The time taken to meet is

A. 2 s
B. 4 s
C. 5 s
D. 10 s

Correct Answer: B

Trigger

Meeting problem

Formula / Tool

Time = Separation / Relative Speed

Quick Execution

100 / (10 + 15)

= 100 / 25

= 4 s

Trap: Using speed difference instead of sum.

RM-17

Two cars are 120 m apart and move in the same direction with speeds of 30 m/s and 20 m/s. The faster car catches the slower car after

A. 10 s
B. 12 s
C. 15 s
D. 20 s

Correct Answer: B

Trigger

Catch-up problem

Formula / Tool

Time = Separation / Relative Speed

Quick Execution

120 / (30 − 20)

= 120 / 10

= 12 s

Trap: Adding speeds instead of subtracting.

RM-18

A train moves at 60 km/h. A man walks at 6 km/h in the same direction. The train's speed relative to the man is

A. 54 km/h
B. 60 km/h
C. 66 km/h
D. 72 km/h

Correct Answer: A

Trigger

Relative speed

Formula / Tool

Velocity Difference

Quick Execution

60 − 6

= 54 km/h

Trap: Adding speeds instead of subtracting.

RM-19

Two particles have accelerations of 5 m/s² and 3 m/s² in opposite directions. The magnitude of their relative acceleration is

A. 2 m/s²
B. 3 m/s²
C. 5 m/s²
D. 8 m/s²

Correct Answer: D

Trigger

Relative acceleration

Formula / Tool

a_AB = a_A − a_B

Quick Execution

Opposite directions

5 + 3

= 8 m/s²

Trap: Subtracting accelerations automatically.

RM-20

A boat moves at 5 m/s in still water. The river current speed is 3 m/s. Its speed relative to the bank while moving downstream is

A. 2 m/s
B. 3 m/s
C. 5 m/s
D. 8 m/s

Correct Answer: D

Trigger

Downstream motion

Formula / Tool

Velocity Addition

Quick Execution

5 + 3

= 8 m/s

Trap: Reporting boat speed only.

RM-21

A boat moves at 5 m/s in still water. The river current speed is 3 m/s. Its speed relative to the bank while moving upstream is

A. 2 m/s
B. 3 m/s
C. 5 m/s
D. 8 m/s

Correct Answer: A

Trigger

Upstream motion

Formula / Tool

Velocity Subtraction

Quick Execution

5 − 3

= 2 m/s

Trap: Adding speeds irrespective of direction.

RM-22

Rain falls vertically downward with speed v. A man runs horizontally with speed v. The rain appears to the man to fall

A. Vertically
B. Horizontally
C. Along an inclined path
D. At rest

Correct Answer: C

Trigger

Observer frame

Formula / Tool

Relative Velocity

Quick Execution

Relative velocity has horizontal and vertical components.

Rain appears inclined.

Trap: Using the ground frame.

RM-23

The velocity of an object relative to itself is

A. −v
B. v
C. 2v
D. 0

Correct Answer: D

Trigger

Reference frame recognition

Formula / Tool

Relative Velocity

Quick Execution

v − v

= 0

Trap: Assuming every moving object has non-zero relative velocity.

RM-24

Two trains move with equal speeds v in opposite directions. Their relative speed is

A. 0
B. v
C. 2v
D. 4v

Correct Answer: C

Trigger

Opposite-direction motion

Formula / Tool

Relative Velocity

Quick Execution

v + v

= 2v

Trap: Using subtraction instead of addition.

RM-25

A faster runner starts 50 m behind a slower runner. If their relative speed is 5 m/s, the catch-up time is

A. 5 s
B. 10 s
C. 15 s
D. 20 s

Correct Answer: B

Trigger

Catch-up problem

Formula / Tool

Time = Separation / Relative Speed

Quick Execution

50 / 5

= 10 s

Trap: Using actual speed instead of relative speed.

RM-01

RM-02

RM-03

RM-04

RM-05

RM-06

RM-07

RM-08

RM-09

RM-10

RM-11

RM-12

RM-13

RM-14

RM-15

RM-16

RM-17

RM-18

RM-19

RM-20

RM-21

RM-22

RM-23

RM-24

RM-25

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Vertical Motion

Pursuit Problems

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