Instability Analysis

Physics becomes difficult when students assume that one quantity completely determines another.

Many famous mistakes arise from such assumptions.

This chapter teaches how to recognize unstable states.

IA-1 : Zero-State Instability

Zero velocity is not a stable conclusion.

A particle can have v = 0 and still possess non-zero acceleration.

MCQ-01

At the highest point of a vertically projected ball,

• A. Velocity and acceleration are both zero
• B. Velocity is zero but acceleration is non-zero
• C. Velocity is non-zero and acceleration is zero
• D. Both velocity and acceleration are non-zero

MCQ-09

A particle has zero velocity at an instant. Which statement is necessarily true?

• A. Acceleration is zero
• B. Motion has ended
• C. Velocity is zero at that instant
• D. Displacement is zero

MCQ-11

A velocity–time graph crosses the time axis. At the crossing instant,

• A. Displacement becomes zero
• B. Acceleration becomes zero
• C. Velocity becomes zero
• D. Motion ends

MCQ-19

A particle has zero velocity and non-zero acceleration. Such a situation is

• A. Impossible
• B. Possible
• C. Possible only in circular motion
• D. Possible only at rest

IA-2 : Sign Instability

The sign of acceleration alone never determines whether a particle speeds up or slows down.

Speed depends on the signs of both velocity and acceleration.

Golden Sign Rule

MCQ-02

A particle has velocity −10 m/s and acceleration −2 m/s². The particle is

• A. Slowing down
• B. Speeding up
• C. At rest
• D. Moving with constant speed

MCQ-03

A particle has velocity +10 m/s and acceleration −2 m/s². The particle is

• A. Speeding up
• B. Slowing down
• C. At rest
• D. Moving backward

MCQ-04

A particle has velocity −10 m/s and acceleration +2 m/s². The particle is

• A. Speeding up
• B. Slowing down
• C. At rest
• D. Moving forward

MCQ-12

A particle moves in the negative direction while speeding up. Which combination is possible?

• A. v > 0, a < 0
• B. v < 0, a < 0
• C. v < 0, a > 0
• D. v > 0, a > 0

MCQ-15

A particle has positive acceleration. Which statement must be true?

• A. It moves in the positive direction
• B. It speeds up
• C. Acceleration is positive
• D. Velocity is positive

MCQ-16

A particle has negative velocity and negative acceleration. Which quantity definitely increases?

• A. Position
• B. Speed
• C. Displacement
• D. Time

MCQ-18

A particle moving east can have acceleration west and still continue moving east.

• A. True
• B. False
• C. Only in vacuum
• D. Depends on mass

MCQ-20

A particle's velocity changes from −10 m/s to −20 m/s. The speed is

• A. Decreasing
• B. Constant
• C. Increasing
• D. Zero

IA-3 : State-Collapse Instability

Students often collapse multiple physical states into one.

These are among the most common conceptual mistakes in kinematics.

MCQ-05

A particle moves 10 m east and then 10 m west. Its displacement is

• A. 0 m
• B. 10 m
• C. 20 m
• D. 30 m

MCQ-06

Two particles are at the same position at a given instant. Which statement is necessarily true?

• A. Their velocities are equal
• B. Their accelerations are equal
• C. Their positions are equal
• D. Their future motions are identical

MCQ-07

Two particles have the same velocity at an instant. Which statement must be true?

• A. Their accelerations are equal
• B. Their positions are equal
• C. Their velocities are equal
• D. Their future paths are identical

MCQ-14

A particle's displacement is zero after a journey. Which statement must be true?

• A. Distance travelled is zero
• B. Motion never occurred
• C. Initial and final positions coincide
• D. Velocity remained zero throughout

MCQ-17

Two position–time graphs intersect. At that instant,

• A. Velocities are equal
• B. Accelerations are equal
• C. Positions are equal
• D. Motions are identical

IA-4 : Constant-Speed Instability

Constant speed does not imply zero acceleration.

Zero acceleration does not imply rest.

MCQ-08

A particle has zero acceleration. Which statement must be true?

• A. Velocity is zero
• B. Position is zero
• C. Velocity is constant
• D. The particle is at rest

MCQ-10

A body moving with constant speed can still have acceleration if

• A. Its direction changes
• B. Its mass changes
• C. Its displacement is zero
• D. Its speed becomes zero

IA-5 : Relative-State Instability

Two objects may be moving continuously and still have zero relative velocity.

Motion itself does not guarantee relative motion.

MCQ-13

Two cars move in the same direction with equal speeds. Their relative velocity is

• A. Equal to their speed
• B. Twice their speed
• C. Zero
• D. Cannot be determined

Instability Master Snapshot

What You Have Learned

• Zero velocity does not imply zero acceleration.
• The signs of velocity and acceleration determine whether speed increases or decreases.
• Same position does not imply same motion.
• Same velocity does not imply same future behaviour.
• Zero displacement does not imply zero distance travelled.
• Constant speed does not imply zero acceleration.
• Moving objects can have zero relative velocity.