Pursuit Analysis

PP-01

A car moving at 20 m/s is 100 m behind a bus moving at 15 m/s. The time required for the car to catch the bus is

A. 10 s
B. 15 s
C. 20 s
D. 25 s

Correct Answer: C

Trigger

Direct pursuit

Formula / Tool

Relative Speed

Quick Execution

t = 100/(20−15)

= 100/5

= 20 s

Trap: Adding speeds instead of subtracting them.

PP-02

A runner moving at 8 m/s chases another runner moving at 8 m/s. If the lead is 20 m, the chasing runner will

A. Catch up after 2.5 s
B. Catch up after 5 s
C. Catch up after 10 s
D. Never catch up

Correct Answer: D

Trigger

Equal-speed pursuit

Formula / Tool

Relative Speed

Quick Execution

Relative speed

= 8 − 8

= 0

No catch possible

Trap: Applying distance ÷ speed blindly.

PP-03

A cyclist moving at 12 m/s is behind another cyclist moving at 15 m/s. The separation between them will

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

Correct Answer: C

Trigger

Gap evolution

Formula / Tool

Relative Velocity Sign

Quick Execution

Rear cyclist is slower.

Gap keeps increasing.

Trap: Assuming every chase ends in a catch.

PP-04

A thief runs at 6 m/s. A police officer starts chasing 10 s later and runs at 8 m/s. The lead gained by the thief before the chase begins is

A. 20 m
B. 40 m
C. 60 m
D. 80 m

Correct Answer: C

Trigger

Delayed pursuit

Formula / Tool

Distance = Speed × Time

Quick Execution

Distance

= 6 × 10

= 60 m

Trap: Starting relative-speed calculations immediately.

PP-05

A car moving at 25 m/s pursues a truck moving at 20 m/s. If the initial gap is doubled, the catch-up time will

A. Halve
B. Remain the same
C. Double
D. Quadruple

Correct Answer: C

Trigger

Pursuit scaling

Formula / Tool

t = d / v_rel

Quick Execution

Distance doubles.

Relative speed unchanged.

Time doubles.

Trap: Assuming relative speed also changes.

PP-06

A faster runner is 30 m behind a slower runner. If their relative speed is 3 m/s, the catch-up time is

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

Correct Answer: B

Trigger

Closing speed recognition

Formula / Tool

Relative Speed

Quick Execution

t = 30/3

= 10 s

Trap: Using the sum of speeds.

PP-07

Two vehicles move in the same direction. The rear vehicle is faster than the front vehicle. At the instant they meet, which quantity becomes zero?

A. Individual speeds
B. Relative speed
C. Separation
D. Acceleration

Correct Answer: C

Trigger

Catch event

Formula / Tool

Pursuit Interpretation

Quick Execution

Meeting condition:

Separation = 0

Trap: Confusing meeting with equal speeds.

PP-08

A car moving at 18 m/s is chasing another car moving at 12 m/s. A toll gate is 90 m ahead of the slower car, and the faster car is 30 m behind it. Will the faster car catch the slower car before the toll gate?

A. Yes
B. No
C. Only if speeds increase
D. Cannot be determined

Correct Answer: A

Trigger

Catch-before-boundary

Formula / Tool

Relative Speed + Accessibility

Quick Execution

Catch time

= 30/(18−12)

= 5 s

Slower car reaches gate in

90/12 = 7.5 s

5 < 7.5

Catch occurs first

Trap: Checking only one motion instead of both.

PP-09

A car starts from rest and accelerates uniformly. A cyclist moving with constant speed passes it. Initially the gap increases, but later it decreases. This happens because

A. The cyclist accelerates
B. The car's speed eventually exceeds the cyclist's speed
C. The cyclist slows down
D. Relative speed is always zero

Correct Answer: B

Trigger

Accelerated pursuit

Formula / Tool

Relative Velocity Evolution

Quick Execution

Car speed keeps increasing.

Eventually

Car speed > Cyclist speed

Gap starts decreasing.

Trap: Assuming the gap must always increase or always decrease.

PP-10

Runner A is 50 m ahead of Runner B. Runner A runs at 5 m/s, while Runner B runs at 10 m/s. At the instant B catches A, the distance covered by B is

A. 25 m
B. 50 m
C. 75 m
D. 100 m

Correct Answer: D

Trigger

Interception condition

Formula / Tool

Relative Speed

Quick Execution

Catch time

= 50/(10−5)

= 10 s

Distance covered by B

= 10 × 10

= 100 m

Trap: Using the initial gap as the distance covered by B.

PP-11

A thief runs at 5 m/s and gets a head start of 100 m. A police officer runs at 10 m/s. The time required to catch the thief is

A. 10 s
B. 15 s
C. 20 s
D. 25 s

Correct Answer: C

Trigger

Delayed pursuit

Formula / Tool

Relative Speed

Quick Execution

t = 100/(10−5)

= 100/5

= 20 s

Trap: Using police speed instead of relative speed.

PP-12

A train moving at 30 m/s pursues another train moving at 20 m/s. If the initial separation is 500 m, the catch-up time is

A. 25 s
B. 50 s
C. 75 s
D. 100 s

Correct Answer: B

Trigger

Train pursuit

Formula / Tool

Relative Speed

Quick Execution

t = 500/(30−20)

= 500/10

= 50 s

Trap: Adding train speeds.

PP-13

A dog runs at 12 m/s chasing a man running at 8 m/s. If the man is initially 40 m ahead, the catch-up time is

A. 5 s
B. 8 s
C. 10 s
D. 12 s

Correct Answer: C

Trigger

Animal pursuit

Formula / Tool

Relative Speed

Quick Execution

t = 40/(12−8)

= 40/4

= 10 s

Trap: Using dog speed directly.

PP-14

Two runners move on a circular track. Runner A completes one lap in 40 s. Runner B completes one lap in 50 s. The time after which A first overtakes B is

A. 100 s
B. 150 s
C. 200 s
D. 250 s

Correct Answer: C

Trigger

Circular-track pursuit

Formula / Tool

Relative Lap Rate

Quick Execution

Relative rate

= 1/40 − 1/50

= 1/200

Time = 200 s

Trap: Subtracting lap times instead of lap rates.

PP-15

A car is 60 m behind a truck. The car moves at 25 m/s and the truck at 20 m/s. How far will the car travel before catching the truck?

A. 200 m
B. 250 m
C. 300 m
D. 350 m

Correct Answer: C

Trigger

Catch distance

Formula / Tool

Relative Speed

Quick Execution

Catch time

= 60/(25−20)

= 12 s

Distance by car

= 25 × 12

= 300 m

Trap: Reporting the initial separation instead of the distance travelled.

PP-16

A runner is 40 m ahead and runs at 6 m/s. A chaser runs at 10 m/s. The distance covered by the runner before being caught is

A. 40 m
B. 50 m
C. 60 m
D. 80 m

Correct Answer: C

Trigger

Target distance

Formula / Tool

Catch-Up Analysis

Quick Execution

t = 40/(10−6)

= 10 s

Distance by runner

= 6 × 10

= 60 m

Trap: Calculating the distance covered by the chaser instead.

PP-17

A car catches a bus in 20 s. If the relative speed becomes twice as large, the catch-up time becomes

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

Correct Answer: B

Trigger

Scaling law

Formula / Tool

t ∝ 1/v_rel

Quick Execution

Relative speed doubles

Time halves

20/2

= 10 s

Trap: Assuming catch-up time remains unchanged.

PP-18

For the same relative speed, if the initial gap is reduced to half, the catch-up time becomes

A. One-fourth
B. Half
C. Same
D. Double

Correct Answer: B

Trigger

Distance scaling

Formula / Tool

t = d/v_rel

Quick Execution

Distance halves

Relative speed unchanged

Time halves

Trap: Thinking relative speed changes too.

PP-19

A cyclist moves at constant speed. A car starts from rest behind it and accelerates uniformly. Initially the gap increases and later decreases because

A. Relative speed changes sign
B. Relative speed remains constant
C. Cyclist accelerates
D. Car decelerates

Correct Answer: A

Trigger

Accelerated pursuit

Formula / Tool

Relative Velocity Evolution

Quick Execution

Initially

Car speed < Cyclist speed

Later

Car speed > Cyclist speed

Relative speed changes sign

Trap: Assuming pursuit requires constant relative speed.

PP-20

Two runners are separated by 100 m. Their relative speed is 4 m/s. The minimum time required for one to catch the other is

A. 20 s
B. 25 s
C. 30 s
D. 40 s

Correct Answer: B

Trigger

Direct closing-speed recognition

Formula / Tool

t = d/v_rel

Quick Execution

100/4

= 25 s

Trap: Using individual speed instead of relative speed.

PP-01

PP-02

PP-03

PP-04

PP-05

PP-06

PP-07

PP-08

PP-09

PP-10

PP-11

PP-12

PP-13

PP-14

PP-15

PP-16

PP-17

PP-18

PP-19

PP-20

Continue Learning

Relative Motion

Accessibility Questions

Reversal of Motion

Multi-Stage Motion