Chapter Home Revision Handbook Concept Clarity 20-Second Challenge PYQ Masterclass
APPLICATION MASTERCLASS 09

Calculus-Differentiation

20-Second Physics Challenge
Trigger Recognition & Trap Elimination

Graph-Diff-A : Position–Time Graph

Graph Differentiation A

Answer GD-01 to GD-05 using this graph.

GD-01

Refer Graph-Diff-A. At which point is the velocity zero?

  • A. A
  • B. B
  • C. C
  • D. P
Correct Answer: D

Trigger

Zero slope on position–time graph

Formula

Velocity = Slope of x–t graph

Execution

At P,

Slope = 0

Velocity = 0
Trap: Choosing the highest position instead of checking the slope.

GD-02

Refer Graph-Diff-A. At which point is the velocity negative?

  • A. A
  • B. B
  • C. P
  • D. C
Correct Answer: D

Trigger

Negative slope

Formula

Velocity = Slope of x–t graph

Execution

At C,

Slope < 0

Velocity < 0
Trap: Thinking velocity becomes negative only when position becomes negative.

GD-03

Refer Graph-Diff-A. Which points have positive velocity?

  • A. A only
  • B. B only
  • C. A and B
  • D. P and C
Correct Answer: C

Trigger

Positive slope

Formula

Velocity = Slope of x–t graph

Execution

At A and B,

Slope > 0

Velocity > 0
Trap: Confusing position value with velocity.

GD-04

Refer Graph-Diff-A. At which point is the velocity greatest?

  • A. A
  • B. B
  • C. P
  • D. C
Correct Answer: A

Trigger

Compare graph slopes

Formula

Velocity ∝ Slope

Execution

Point A has the steepest positive slope.

Therefore,

vA is maximum.
Trap: Comparing graph height instead of slope.

GD-05

Refer Graph-Diff-A. Which point represents motion in the negative direction?

  • A. A
  • B. B
  • C. P
  • D. C
Correct Answer: D

Trigger

Direction from velocity sign

Formula

Velocity sign = Slope sign

Execution

At C,

Slope < 0

Velocity < 0
Trap: Using position sign instead of velocity sign.

GD-06

Refer Graph-Diff-A. At which point is the particle momentarily at rest?

Correct Answer: D

Trigger

Momentarily at rest

Formula

Velocity = Slope of x–t graph

Execution

At P,

Slope = 0

Velocity = 0
Trap: Assuming the particle is permanently at rest.

GD-07

Refer Graph-Diff-A. As the particle moves from A to B, the particle is

Correct Answer: B

Trigger

Change in graph slope

Formula

Velocity = Slope of x–t graph

Execution

Slope at A > Slope at B

Velocity decreases
Trap: Looking at position values instead of slope values.

GD-08

Refer Graph-Diff-A. As the particle moves from B to P, its velocity

Correct Answer: B

Trigger

Slope evolution

Formula

Velocity = Slope of x–t graph

Execution

Positive slope

↓

Smaller positive slope

↓

Zero slope at P
Trap: Assuming increasing position means increasing velocity.

Graph-Diff-B : Velocity–Time Graph

Graph Differentiation B

GD-09

Refer Graph-Diff-B. At point A, the acceleration is

Correct Answer: C

Trigger

Slope of velocity–time graph

Formula

Acceleration = Slope of v–t graph

Execution

At A,

Graph is horizontal

Slope = 0

Acceleration = 0
Trap: Using graph height instead of slope.

GD-10

Refer Graph-Diff-B. At point B, the acceleration is

Correct Answer: A

Trigger

Positive graph slope

Formula

Acceleration = Slope of v–t graph

Execution

Region-II rises with time

Slope > 0

Acceleration > 0
Trap: Looking at velocity instead of slope.

GD-11

Refer Graph-Diff-B. At point C, the acceleration is

Correct Answer: C

Trigger

Horizontal v–t graph

Formula

Acceleration = Slope of v–t graph

Execution

At C,

Slope = 0

Acceleration = 0
Trap: Assuming non-zero velocity means non-zero acceleration.

GD-12

Refer Graph-Diff-B. In which region is the acceleration positive?

Correct Answer: B

Trigger

Positive slope region

Formula

Acceleration = Slope

Execution

Region-I → Slope = 0

Region-II → Slope > 0

Region-III → Slope = 0
Trap: Confusing velocity value with acceleration.

GD-13

Refer Graph-Diff-B. Which region represents motion with constant velocity?

Correct Answer: C

Trigger

Horizontal v–t graph

Formula

Constant velocity ⇔ Horizontal v–t graph

Execution

Region-I is horizontal

Region-III is horizontal

Velocity remains constant
Trap: Choosing Region-II because velocity is increasing.

GD-14

Refer Graph-Diff-B. Which region contributes the greatest displacement?

Correct Answer: C

Trigger

Largest area under v–t graph

Formula

Displacement = Area under v–t graph

Execution

Region-III has the largest rectangular area.
Trap: Comparing graph heights instead of areas.

GD-15

Refer Graph-Diff-B. The displacement during Region-I is represented by

Correct Answer: C

Trigger

Area interpretation

Formula

Displacement = Area under v–t graph

Execution

Region-I displacement = Area of Region-I
Trap: Using slope, which represents acceleration.

GD-16

Refer Graph-Diff-B. Compared to Region-I, the displacement during Region-II is

Correct Answer: A

Trigger

Compare graph areas

Formula

Displacement ∝ Area

Execution

Region-II contains more shaded area than Region-I.
Trap: Comparing only velocity values.

GD-17

Refer Graph-Diff-B. The total displacement from O to C is

Correct Answer: D

Trigger

Total area concept

Formula

Total Displacement = Total Area under v–t graph

Execution

Region-I + Region-II + Region-III
Trap: Considering only the final region.

GD-18

Refer Graph-Diff-B. The shaded region under the graph represents

Correct Answer: C

Trigger

Area under velocity–time graph

Formula

Displacement = Area under v–t graph

Execution

Entire shaded area represents displacement.
Trap: Confusing area with slope.

Continue Learning

Complete the Graph Intelligence journey and move to instability-based thinking.

Graph Intelligence

Master slope, area, velocity, acceleration, and displacement from graphs.

Instability

Learn zero-velocity states, sign traps, and motion paradoxes.