Motion in a Plane explains how objects move in two dimensions using vectors. Important Questions Class 11 Physics Chapter 3 help students understand displacement, velocity, acceleration, projectile motion and circular motion.
Important Questions Class 11 Physics Chapter 3 help students practise Motion in a Plane through concept-based questions, formulas, numericals and exam-style answers.
This chapter builds the foundation for mechanics because students learn how to describe motion using vector quantities. It also shows how two-dimensional motion can be split into horizontal and vertical components.
Students should use these questions to revise scalars, vectors, vector addition, resolution of vectors, projectile motion and uniform circular motion. The chapter is important for 2026 exams because it includes both reasoning questions and formula-based numericals.
Key Takeaways from Important Questions Class 11 Physics Chapter 3
| Area |
What Students Should Revise |
| Chapter Name |
Motion in a Plane |
| Chapter Number |
Chapter 3 |
| Main Idea |
Motion in two dimensions using vectors |
| Core Topics |
Scalars, vectors, vector addition, resolution, projectile motion |
| Important Numericals |
Projectile range, maximum height, time of flight, centripetal acceleration |
| Important Formulas |
Vector components, projectile equations, circular motion formulas |
| High-Scoring Areas |
Projectile motion and uniform circular motion |
| Common Mistake |
Using scalar addition for vector quantities |
| Best Practice |
Draw diagrams and resolve vectors before solving |
Motion in a Plane Formulas Class 11
Students should revise motion in a plane formulas class 11 before solving numericals. Most questions come from vector components, projectile motion and uniform circular motion.
| Concept |
Formula |
| Vector components |
Ax = A cosθ, Ay = A sinθ |
| Magnitude of vector |
A = √(Ax² + Ay²) |
| Direction of vector |
tanθ = Ay/Ax |
| Position vector in plane |
r = xi + yj |
| Displacement |
Δr = r′ − r |
| Average velocity |
vavg = Δr/Δt |
| Velocity components |
vx = dx/dt, vy = dy/dt |
| Acceleration components |
ax = dvx/dt, ay = dvy/dt |
| Velocity under constant acceleration |
v = v₀ + at |
| Position under constant acceleration |
r = r₀ + v₀t + 1/2 at² |
| Projectile x-coordinate |
x = u cosθ × t |
| Projectile y-coordinate |
y = u sinθ × t − 1/2 gt² |
| Time of flight |
T = 2u sinθ/g |
| Maximum height |
H = u² sin²θ/2g |
| Horizontal range |
R = u² sin2θ/g |
| Centripetal acceleration |
ac = v²/R |
| Angular speed relation |
v = ωR |
| Circular acceleration |
ac = ω²R |
Motion in a Plane Class 11 Important Questions on Scalars and Vectors
Motion in a plane class 11 important questions begin with scalars and vectors. This section matters because every later topic uses vector direction.
Q1. What is a scalar quantity?
A scalar quantity has magnitude only. It does not need direction.
Examples include mass, distance, speed, time, temperature and volume.
Q2. What is a vector quantity?
A vector quantity has both magnitude and direction. It also follows vector addition rules.
Examples include displacement, velocity, acceleration and force.
Q3. Why is displacement a vector?
Displacement has magnitude and direction. It gives the straight-line change from initial position to final position.
Q4. Why is distance a scalar quantity?
Distance has only magnitude. It tells the total path length covered by an object.
Q5. Can displacement be zero when distance is not zero?
Yes. If an object returns to its starting point, displacement becomes zero. Distance remains equal to the total path covered.
Q6. Give two examples each of scalar and vector quantities.
Mass and speed are scalar quantities. Velocity and acceleration are vector quantities.
Scalars and Vectors Class 11 Questions with Answers
Scalars and vectors class 11 questions often test comparison. Students should not write only that a vector has direction. They should also mention vector addition rules.
Q7. State one difference between speed and velocity.
Speed is scalar because it has only magnitude. Velocity is vector because it has magnitude and direction.
Q8. Is pressure a scalar or vector?
Pressure is scalar. It has magnitude but no direction.
Q9. Is angular velocity a scalar or vector?
Angular velocity is a vector quantity. Its direction follows the axis of rotation.
Q10. Why are vectors not added by ordinary algebra?
Vectors have direction. Their addition depends on both magnitude and direction.
Q11. What is a null vector?
A null vector has zero magnitude. Its direction is not defined.
Q12. Give one physical example of a null vector.
If a particle returns to its starting point, its displacement vector is zero.
Vector Addition Class 11 Questions
Vector addition class 11 questions test graphical and analytical methods. Students should know triangle law, parallelogram law and component method.
Q13. State the triangle law of vector addition.
If two vectors form two sides of a triangle in order, their resultant is the third side taken from the tail of the first vector to the head of the second vector.
Q14. State the parallelogram law of vector addition.
If two vectors start from the same point and form adjacent sides of a parallelogram, the diagonal through that point gives the resultant.
Q15. Is vector addition commutative?
Yes. Vector addition is commutative.
A + B = B + A
Q16. Is vector addition associative?
Yes. Vector addition is associative.
(A + B) + C = A + (B + C)
Q17. What is vector subtraction?
Vector subtraction means adding the negative of a vector.
A − B = A + (−B)
Q18. When is the resultant of two equal vectors zero?
The resultant is zero when two equal vectors act in opposite directions.
Resolution of Vectors Class 11 Questions
Resolution of vectors class 11 questions are important for projectile motion. Resolution helps split one vector into perpendicular components.
Q19. What is resolution of a vector?
Resolution of a vector means splitting it into components along chosen directions.
Q20. What are rectangular components of a vector?
Rectangular components are components of a vector along mutually perpendicular axes.
Q21. If vector A makes angle θ with x-axis, write its components.
The components are:
Ax = A cosθ
Ay = A sinθ
Q22. How do you find magnitude from components?
Magnitude is:
A = √(Ax² + Ay²)
Q23. How do you find direction from components?
Direction is found from:
tanθ = Ay/Ax
Q24. Why do we resolve projectile velocity into components?
Projectile motion has independent horizontal and vertical motions. Components make equations easier.
Class 11 Physics Chapter 3 Questions and Answers on Position, Velocity and Acceleration
Class 11 physics chapter 3 questions and answers often test vector form of position, velocity and acceleration. These questions connect vectors with motion.
Q25. Write the position vector of a particle in a plane.
The position vector is:
r = xi + yj
Here, x and y are coordinates of the particle.
Q26. What is displacement vector?
Displacement vector is the change in position vector.
Δr = r′ − r
Q27. Define average velocity in a plane.
Average velocity is displacement divided by time interval.
vavg = Δr/Δt
Q28. What is the direction of instantaneous velocity?
Instantaneous velocity acts along the tangent to the path at that point.
Q29. Can velocity and acceleration have different directions in plane motion?
Yes. In two-dimensional motion, velocity and acceleration can act in different directions.
Q30. Why is circular motion accelerated motion?
Circular motion has changing velocity direction. So, acceleration exists even if speed remains constant.
Motion in a Plane Numericals Class 11
Motion in a plane numericals class 11 need careful use of x and y components. Start by writing given values and direction.
Q31. A vector has components 6 m and 8 m. Find its magnitude.
A = √(6² + 8²)
A = √(36 + 64)
A = √100
A = 10 m
Answer: Magnitude is 10 m.
Q32. A vector of magnitude 20 N makes 60° with x-axis. Find its components.
Ax = A cosθ = 20 cos60° = 10 N
Ay = A sinθ = 20 sin60° = 10√3 N
Answer: Components are 10 N and 10√3 N.
Q33. A particle has position r = 3t i + 4t j. Find velocity.
Velocity is derivative of position.
v = dr/dt
v = 3i + 4j
Magnitude = √(3² + 4²) = 5 m s⁻¹
Answer: Velocity is 3i + 4j m s⁻¹, and speed is 5 m s⁻¹.
Q34. A particle moves with velocity 5i + 12j m s⁻¹. Find speed.
Speed = √(5² + 12²)
Speed = √169
Speed = 13 m s⁻¹
Answer: Speed is 13 m s⁻¹.
Projectile Motion Class 11 Questions
Projectile motion class 11 questions are among the most important parts of Chapter 3. Projectile motion combines horizontal uniform motion and vertical motion under gravity.
Q35. What is projectile motion?
Projectile motion is the motion of an object thrown into the air under gravity after projection.
Examples include a cricket ball, football or stone thrown at an angle.
Q36. Why is projectile motion two-dimensional?
Projectile motion has horizontal and vertical components. The object moves in a plane.
Q37. What is the shape of a projectile path?
The path of a projectile is a parabola.
Q38. Why does the horizontal velocity of a projectile remain constant?
No horizontal acceleration acts if air resistance is neglected. So, horizontal velocity remains constant.
Q39. Why does vertical velocity change during projectile motion?
Gravity acts vertically downward. So, the vertical component of velocity changes with time.
Q40. What is the acceleration of a projectile?
The acceleration is g downward.
In vector form:
a = −gj
Projectile Motion Numericals Class 11
Projectile motion numericals class 11 usually test time of flight, range, maximum height and velocity components.
Q41. A ball is projected with speed 20 m s⁻¹ at 30°. Find horizontal and vertical components.
ux = u cosθ = 20 cos30° = 10√3 m s⁻¹
uy = u sinθ = 20 sin30° = 10 m s⁻¹
Answer: Horizontal component is 10√3 m s⁻¹. Vertical component is 10 m s⁻¹.
Q42. Find time of flight for u = 20 m s⁻¹ and θ = 30°. Take g = 10 m s⁻².
T = 2u sinθ/g
T = 2 × 20 × 1/2 / 10
T = 2 s
Answer: Time of flight is 2 s.
Q43. Find maximum height for u = 20 m s⁻¹ and θ = 30°. Take g = 10 m s⁻².
H = u² sin²θ/2g
H = 20² × (1/2)² / 20
H = 400 × 1/4 / 20
H = 5 m
Answer: Maximum height is 5 m.
Q44. Find horizontal range for u = 20 m s⁻¹ and θ = 30°. Take g = 10 m s⁻².
R = u² sin2θ/g
R = 400 × sin60° / 10
R = 40 × √3/2
R = 20√3 m
Answer: Horizontal range is 20√3 m.
Q45. At what angle is the range maximum for a given speed?
The range is maximum at 45° when the projectile lands at the same level.
Class 11 Physics Motion in a Plane Important Questions on Projectile Concepts
These class 11 physics motion in a plane important questions help students answer reasoning questions clearly.
Q46. Why is projectile motion treated as two independent motions?
Horizontal and vertical motions do not affect each other. Gravity acts only in the vertical direction.
Q47. What happens to vertical velocity at maximum height?
Vertical velocity becomes zero at maximum height.
Q48. Is acceleration zero at maximum height?
No. Acceleration remains g downward at maximum height.
Q49. Why are ranges equal for angles 30° and 60°?
Projectile range depends on sin2θ. Since sin60° and sin120° are equal, ranges are equal.
Q50. Does projectile speed become zero at maximum height?
No. Only vertical velocity becomes zero. Horizontal velocity remains present.
Q51. What happens if a projectile is thrown horizontally?
Its initial vertical velocity is zero. It still falls due to gravity while moving horizontally.
Uniform Circular Motion Class 11 Questions
Uniform circular motion class 11 questions test direction changes in velocity. Students should remember that speed stays constant but velocity changes.
Q52. What is uniform circular motion?
Uniform circular motion is motion along a circular path with constant speed.
Q53. Why is uniform circular motion accelerated?
Velocity direction changes continuously. So, acceleration acts even at constant speed.
Q54. What is centripetal acceleration?
Centripetal acceleration is acceleration directed towards the centre of the circular path.
Q55. Write the formula for centripetal acceleration.
The formula is:
ac = v²/R
Q56. What is angular speed?
Angular speed is the rate of change of angular displacement.
ω = Δθ/Δt
Q57. What is the relation between linear speed and angular speed?
The relation is:
v = ωR
Q58. Is centripetal acceleration a constant vector in uniform circular motion?
No. Its magnitude remains constant, but its direction changes continuously.
Centripetal Acceleration Class 11 Questions
Centripetal acceleration class 11 questions are common in short-answer and numerical formats.
Q59. A body moves in a circle of radius 2 m with speed 10 m s⁻¹. Find centripetal acceleration.
ac = v²/R
ac = 10²/2
ac = 50 m s⁻²
Answer: Centripetal acceleration is 50 m s⁻².
Q60. A stone completes 10 revolutions in 20 s. Find frequency.
Frequency = revolutions/time
Frequency = 10/20
Frequency = 0.5 Hz
Answer: Frequency is 0.5 Hz.
Q61. A particle moves in a circle of radius 0.5 m with angular speed 4 rad s⁻¹. Find centripetal acceleration.
ac = ω²R
ac = 4² × 0.5
ac = 16 × 0.5
ac = 8 m s⁻²
Answer: Centripetal acceleration is 8 m s⁻².
Q62. Why is centripetal acceleration called centre-seeking acceleration?
It always points towards the centre of the circular path.
Motion in a Plane Class 11 Extra Questions
These motion in a plane class 11 extra questions support revision beyond direct formula use.
Q63. Can a vector have zero magnitude and non-zero direction?
No. A vector with zero magnitude has no fixed direction.
Q64. Can two unequal vectors have equal magnitudes?
Yes. Two vectors may have equal magnitudes but different directions.
Q65. What is the angle between velocity and acceleration in uniform circular motion?
The angle is 90°. Velocity acts tangent to the path, while acceleration acts towards the centre.
Q66. Why does a projectile launched at 45° have maximum range?
Range depends on sin2θ. sin2θ becomes maximum when 2θ = 90°, so θ = 45°.
Q67. What is the range of a projectile launched vertically upward?
The horizontal range is zero because horizontal velocity is zero.
Q68. Can average speed be greater than average velocity magnitude?
Yes. Average speed uses total path length, while average velocity uses displacement.
Q69. When are average speed and average velocity magnitude equal?
They are equal when the object moves along a straight path without changing direction.
Q70. Why should students draw vector diagrams in this chapter?
Vector diagrams show direction clearly. They reduce mistakes in addition, resolution and projectile questions.
Class 11 Physics Chapter 3 Important Questions: Solved Practice Set
This practice set mixes vectors, projectile motion and circular motion. It helps students test full chapter readiness.
Important Questions Class 11 Physics Chapter 3: Mixed Numerical Practice
Use this set after revising formulas. It checks vector components, projectile basics and centripetal acceleration.
Q71. A man walks 3 m east and then 4 m north. Find displacement.
Displacement = √(3² + 4²)
Displacement = 5 m
Direction:
tanθ = 4/3
θ = tan⁻¹(4/3)
Answer: Displacement is 5 m, at angle tan⁻¹(4/3) north of east.
Q72. A body has velocity 8i + 6j m s⁻¹. Find its speed and direction.
Speed = √(8² + 6²)
Speed = √100
Speed = 10 m s⁻¹
tanθ = 6/8 = 3/4
Answer: Speed is 10 m s⁻¹, at angle tan⁻¹(3/4) with x-axis.
Q73. A projectile has time of flight 4 s. Find time taken to reach maximum height.
Time to maximum height = T/2
= 4/2
= 2 s
Answer: It reaches maximum height in 2 s.
Q74. A projectile has maximum height 20 m and range 80 m. Which part of motion gives maximum height?
The vertical component gives maximum height. The horizontal component gives range.
Q75. A particle moves in a circle with speed 6 m s⁻¹ and radius 3 m. Find centripetal acceleration.
ac = v²/R
ac = 36/3
ac = 12 m s⁻²
Answer: Centripetal acceleration is 12 m s⁻².
Common Mistakes in Motion in a Plane Questions and Answers
Students often add vectors like simple numbers. Always consider direction before addition.
Common mistakes include:
- Adding vector magnitudes without checking direction
- Confusing distance with displacement
- Forgetting that projectile acceleration remains downward
- Saying acceleration is zero at maximum height
- Using range formula for unequal landing heights
- Saying uniform circular motion has no acceleration
- Mixing degrees and radians in circular motion
- Skipping vector diagrams before numericals
Distance depends on path. Displacement depends only on initial and final positions.
The standard range formula applies when projectile lands at the same level. Students should check this condition before using it.
Important Questions Class 11 Physics Chapter-Wise