Graph Intelligence

Graph-A : Position–Time Graph

Instructions: Refer Graph-A and answer GI-01 to GI-08.

GI-01

At point A, the velocity of the particle is

A. Positive
B. Zero
C. Negative
D. Cannot be determined

Correct Answer: A

Trigger

Velocity sign

Formula / Tool

Velocity = Slope of x–t graph

Quick Execution

Graph rises with time.

Slope is positive.

Trap: Using graph height instead of graph slope.

GI-02

At point P, the velocity of the particle is

A. Positive
B. Negative
C. Maximum
D. Zero

Correct Answer: D

Trigger

Turning point

Formula / Tool

Velocity = Slope of x–t graph

Quick Execution

Tangent is horizontal.

Slope = 0.

Trap: Confusing maximum position with maximum velocity.

GI-03

At which point is the velocity negative?

A. A
B. B
C. P
D. C

Correct Answer: D

Trigger

Negative slope

Formula / Tool

Velocity Sign Analysis

Quick Execution

Only point C lies on a downward-sloping section.

Trap: Using position sign instead of velocity sign.

GI-04

The particle reverses its direction at

A. A
B. B
C. P
D. C

Correct Answer: C

Trigger

Reversal recognition

Formula / Tool

Velocity changes sign

Quick Execution

Positive slope

↓

Zero slope

↓

Negative slope

Direction changes at P.

Trap: Choosing the first point with negative velocity.

GI-05

At which point is the speed greatest?

A. A
B. B
C. P
D. C

Correct Answer: A

Trigger

Speed magnitude

Formula / Tool

Speed = Magnitude of Slope

Quick Execution

Point A has the steepest tangent.

Trap: Choosing the highest point on the graph.

GI-06

Between A and B, the velocity is

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

Correct Answer: B

Trigger

Slope evolution

Formula / Tool

Velocity = Slope

Quick Execution

Slope becomes less steep.

Velocity decreases.

Trap: Looking at increasing position instead of decreasing slope.

GI-07

At which point is the particle momentarily at rest?

A. A
B. B
C. P
D. C

Correct Answer: C

Trigger

Rest state

Formula / Tool

v = 0 when slope = 0

Quick Execution

Horizontal tangent occurs at P.

Trap: Assuming the particle is at rest because it is at maximum position.

GI-08

Which statement is correct about point C?

A. Position is increasing
B. Velocity is positive
C. Velocity is negative
D. Velocity is zero

Correct Answer: C

Trigger

State extraction

Formula / Tool

Slope Sign Analysis

Quick Execution

Curve slopes downward.

Velocity is negative.

Trap: Reading position value instead of slope.

Graph-B : Velocity–Time Graph

Instructions: Refer Graph-B and answer GI-09 to GI-16.

GI-09

At point A, the velocity of the particle is

A. Positive
B. Zero
C. Negative
D. Cannot be determined

Correct Answer: A

Trigger

Velocity sign

Formula / Tool

Velocity = Graph Height

Quick Execution

Point A lies above the time axis.

Velocity is positive.

Trap: Looking at slope instead of graph height.

GI-10

At point P, the velocity of the particle is

A. Positive
B. Negative
C. Maximum
D. Zero

Correct Answer: D

Trigger

Axis crossing

Formula / Tool

v = 0 at Time-Axis Intersection

Quick Execution

Graph crosses the time axis at P.

v = 0

Trap: Confusing zero velocity with zero acceleration.

GI-11

At point C, the velocity of the particle is

A. Positive
B. Negative
C. Zero
D. Constant

Correct Answer: B

Trigger

Velocity sign

Formula / Tool

Graph Height

Quick Execution

Point C lies below the time axis.

Velocity is negative.

Trap: Using slope sign instead of velocity sign.

GI-12

The acceleration represented by Graph-B is

A. Positive
B. Negative
C. Zero
D. Variable

Correct Answer: B

Trigger

Slope interpretation

Formula / Tool

Acceleration = Slope of v–t Graph

Quick Execution

Graph has constant negative slope.

Acceleration is negative.

Trap: Reading graph height instead of slope.

GI-13

The particle reverses its direction at

A. A
B. B
C. P
D. C

Correct Answer: C

Trigger

Reversal recognition

Formula / Tool

Velocity changes sign

Quick Execution

Positive velocity

↓

Zero velocity

↓

Negative velocity

Direction changes at P.

Trap: Choosing the first point with negative velocity.

GI-14

Region-I represents

A. Negative displacement
B. Positive displacement
C. Negative acceleration
D. Zero velocity

Correct Answer: B

Trigger

Area interpretation

Formula / Tool

Area Under v–t Graph

Quick Execution

Area above the axis

↓

Positive displacement

Trap: Confusing displacement with acceleration.

GI-15

Region-II represents

A. Positive displacement
B. Positive velocity
C. Negative displacement
D. Zero displacement

Correct Answer: C

Trigger

Signed area

Formula / Tool

Area Under v–t Graph

Quick Execution

Area below the axis

↓

Negative displacement

Trap: Ignoring the sign of area.

GI-16

At point B, the particle is

A. Moving in the positive direction and slowing down
B. Moving in the positive direction and speeding up
C. Moving in the negative direction and slowing down
D. At rest

Correct Answer: A

Trigger

Velocity–Acceleration Analysis

Formula / Tool

Sign Analysis

Quick Execution

Velocity > 0

Acceleration < 0

Opposite signs

Speed decreases

Trap: Assuming positive velocity automatically means speeding up.

Graph-C : Velocity–Time Graph

Instructions: Refer Graph-C and answer GI-17 to GI-24.

GI-17

During Stage-I (O to A), the velocity of the particle is

A. 0 m/s
B. 5 m/s
C. 10 m/s
D. 20 m/s

Correct Answer: C

Trigger

Velocity extraction

Formula / Tool

Velocity = Graph Height

Quick Execution

Horizontal line at

10 m/s

Trap: Using graph length instead of graph height.

GI-18

During Stage-I (O to A), the acceleration is

A. Positive
B. Negative
C. Zero
D. Variable

Correct Answer: C

Trigger

Slope interpretation

Formula / Tool

Acceleration = Slope of v–t Graph

Quick Execution

Horizontal line

Slope = 0

Trap: Assuming non-zero velocity implies acceleration.

GI-19

During Stage-II (A to B), the acceleration is

A. Positive
B. Negative
C. Zero
D. Infinite

Correct Answer: A

Trigger

Acceleration sign

Formula / Tool

Slope of v–t Graph

Quick Execution

Velocity increases with time.

Positive slope.

Trap: Reading graph height instead of slope.

GI-20

During Stage-III (B to C), the velocity is

A. 0 m/s
B. 10 m/s
C. 15 m/s
D. 20 m/s

Correct Answer: D

Trigger

Velocity extraction

Formula / Tool

Velocity = Graph Height

Quick Execution

Horizontal line at

20 m/s

Trap: Using average velocity from Stage-II.

GI-21

The displacement during Region-I is

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

Correct Answer: B

Trigger

Area under curve

Formula / Tool

Area = Base × Height

Quick Execution

4 × 10

= 40 m

Trap: Adding velocity and time instead of multiplying.

GI-22

The displacement during Region-II is

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

Correct Answer: C

Trigger

Trapezium area

Formula / Tool

½(a + b) × h

Quick Execution

½(10 + 20) × 4

= 60 m

Trap: Using rectangle area instead of trapezium area.

GI-23

The displacement during Region-III is

A. 40 m
B. 60 m
C. 80 m
D. 100 m

Correct Answer: C

Trigger

Area under curve

Formula / Tool

Area = Base × Height

Quick Execution

4 × 20

= 80 m

Trap: Using Stage-I velocity.

GI-24

The total displacement from O to C is

A. 120 m
B. 160 m
C. 180 m
D. 200 m

Correct Answer: C

Trigger

Total area

Formula / Tool

Total Displacement = Region-I + Region-II + Region-III

Quick Execution

40 + 60 + 80

= 180 m

Trap: Making arithmetic mistakes while summing areas.

Graph-D : Velocity–Time Graph

Instructions: Refer Graph-D and answer GI-25 to GI-36.

GI-25

At point O, the velocity of the particle is

A. −10 m/s
B. 0 m/s
C. 5 m/s
D. 10 m/s

Correct Answer: D

Trigger

Velocity extraction

Formula / Tool

Velocity = Graph Height

Quick Execution

At O,

v = 10 m/s

Trap: Reading slope instead of graph height.

GI-26

At point P, the velocity of the particle is

A. 10 m/s
B. 5 m/s
C. 0 m/s
D. −10 m/s

Correct Answer: C

Trigger

Axis crossing

Formula / Tool

Velocity at Time-Axis Intersection

Quick Execution

At P,

v = 0

Trap: Confusing zero velocity with zero acceleration.

GI-27

At point B, the velocity of the particle is

A. −10 m/s
B. 0 m/s
C. 10 m/s
D. 20 m/s

Correct Answer: A

Trigger

Negative velocity

Formula / Tool

Velocity = Graph Height

Quick Execution

Point B lies below the time axis.

v = −10 m/s

Trap: Ignoring the sign of velocity.

GI-28

The acceleration represented by Graph-D is

A. Positive
B. Negative
C. Zero
D. Variable

Correct Answer: B

Trigger

Slope interpretation

Formula / Tool

Acceleration = Slope of v–t Graph

Quick Execution

Graph has constant negative slope.

Trap: Reading graph height instead of slope.

GI-29

The particle reverses its direction at

A. O
B. P
C. B
D. Never

Correct Answer: B

Trigger

Reversal recognition

Formula / Tool

Velocity changes sign

Quick Execution

Positive velocity

↓

Zero velocity

↓

Negative velocity

Trap: Choosing point B.

GI-30

Region-I represents

A. Negative displacement
B. Positive displacement
C. Zero displacement
D. Negative acceleration

Correct Answer: B

Trigger

Area sign

Formula / Tool

Area Under v–t Graph

Quick Execution

Area above axis

↓

Positive displacement

Trap: Confusing displacement with acceleration.

GI-31

Region-II represents

A. Positive displacement
B. Positive velocity
C. Negative displacement
D. Zero displacement

Correct Answer: C

Trigger

Signed area

Formula / Tool

Area Under v–t Graph

Quick Execution

Area below axis

↓

Negative displacement

Trap: Ignoring the sign of area.

GI-32

If Region-I and Region-II have equal areas, the net displacement is

A. Positive
B. Negative
C. Zero
D. Infinite

Correct Answer: C

Trigger

Net displacement

Formula / Tool

Algebraic Sum of Areas

Quick Execution

Positive Area + Equal Negative Area

= 0

Trap: Adding magnitudes instead of signed areas.

GI-33

If the area of Region-I is 25 m and the area of Region-II is 25 m, the total distance travelled is

A. 0 m
B. 25 m
C. 50 m
D. 75 m

Correct Answer: C

Trigger

Distance calculation

Formula / Tool

Distance = Sum of Magnitudes of Areas

Quick Execution

25 + 25

= 50 m

Trap: Using displacement instead of distance.

GI-34

For Graph-D, which quantity is obtained by adding Region-I and Region-II with their signs?

A. Distance
B. Speed
C. Displacement
D. Acceleration

Correct Answer: C

Trigger

Signed Area Concept

Formula / Tool

Area Under v–t Graph

Quick Execution

Positive and negative areas are added algebraically.

Trap: Confusing distance with displacement.

GI-35

Between O and P, the particle is

A. Moving in the positive direction
B. Moving in the negative direction
C. At rest
D. Reversing continuously

Correct Answer: A

Trigger

Velocity Sign

Formula / Tool

Position Relative to Time Axis

Quick Execution

Graph remains above the time axis.

Velocity is positive.

Trap: Using acceleration sign instead of velocity sign.

GI-36

Between P and B, the particle is

A. Moving in the positive direction
B. Moving in the negative direction
C. At rest
D. Moving with zero acceleration

Correct Answer: B

Trigger

Direction Recognition

Formula / Tool

Velocity Sign

Quick Execution

Graph lies below the time axis.

Velocity is negative.

Trap: Confusing negative velocity with negative acceleration.

Graph-A : Position–Time Graph

GI-01

GI-02

GI-03

GI-04

GI-05

GI-06

GI-07

GI-08

Graph-B : Velocity–Time Graph

GI-09

GI-10

GI-11

GI-12

GI-13

GI-14

GI-15

GI-16

Graph-C : Velocity–Time Graph

GI-17

GI-18

GI-19

GI-20

GI-21

GI-22

GI-23

GI-24

Graph-D : Velocity–Time Graph

GI-25

GI-26

GI-27

GI-28

GI-29

GI-30

GI-31

GI-32

GI-33

GI-34

GI-35

GI-36

Calculus in Physics