Motion Along a Straight Line Problems

This section provides 100 problems to test your understanding of motion along a straight line, including displacement, velocity, acceleration, kinematic equations, and free fall. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence.

Numerical Problems

1. A car travels 200 m in 10 s with constant velocity. Calculate the velocity.

   • (a) $15 , m/s$
   • (b) $20 , m/s$
   • (c) $25 , m/s$
   • (d) $30 , m/s$

2. A particle moves with constant velocity of $5 , m/s$ for 8 s. What is the displacement?

   • (a) $30 , m$
   • (b) $40 , m$
   • (c) $50 , m$
   • (d) $60 , m$

3. A car starts from rest and accelerates at $3 , m/s^2$ for 6 s. Calculate the final velocity.

   • (a) $15 , m/s$
   • (b) $18 , m/s$
   • (c) $21 , m/s$
   • (d) $24 , m/s$

4. A ball is dropped from a height of $45 , m$ ($g = 9.8 , m/s^2$). Calculate the time to reach the ground.

   • (a) $2.5 , s$
   • (b) $3.0 , s$
   • (c) $3.5 , s$
   • (d) $4.0 , s$

5. A car accelerates from $10 , m/s$ to $30 , m/s$ in 5 s. What is the average acceleration?

   • (a) $2 , m/s^2$
   • (b) $4 , m/s^2$
   • (c) $6 , m/s^2$
   • (d) $8 , m/s^2$

6. A particle moves 50 m in 10 s, then 30 m in 5 s in the same direction. Calculate the average velocity.

   • (a) $4 , m/s$
   • (b) $5.3 , m/s$
   • (c) $6 , m/s$
   • (d) $7 , m/s$

7. A ball is thrown upward with an initial velocity of $20 , m/s$ ($g = 9.8 , m/s^2$). Calculate the time to reach the maximum height.

   • (a) $1.5 , s$
   • (b) $2.0 , s$
   • (c) $2.5 , s$
   • (d) $3.0 , s$

8. A car decelerates from $40 , m/s$ to $20 , m/s$ in 4 s. What is the acceleration?

   • (a) $-2 , m/s^2$
   • (b) $-3 , m/s^2$
   • (c) $-4 , m/s^2$
   • (d) $-5 , m/s^2$

9. A stone is dropped from a height of $80 , m$ ($g = 9.8 , m/s^2$). What is the velocity just before hitting the ground?

   • (a) $35 , m/s$
   • (b) $40 , m/s$
   • (c) $45 , m/s$
   • (d) $50 , m/s$

10. A particle starts from rest and accelerates at $4 , m/s^2$ for 3 s. Calculate the displacement.

    • (a) $12 , m$
    • (b) $18 , m$
    • (c) $24 , m$
    • (d) $30 , m$

11. A car moves with constant velocity of $15 , m/s$ for 12 s. What is the distance traveled?

    • (a) $150 , m$
    • (b) $180 , m$
    • (c) $200 , m$
    • (d) $220 , m$

12. A ball is thrown upward with $u = 25 , m/s$ ($g = 9.8 , m/s^2$). What is the maximum height reached?

    • (a) $30 , m$
    • (b) $32 , m$
    • (c) $34 , m$
    • (d) $36 , m$

13. A car accelerates from rest at $5 , m/s^2$ for 4 s, then moves with constant velocity for 2 s. What is the total displacement?

    • (a) $40 , m$
    • (b) $50 , m$
    • (c) $60 , m$
    • (d) $70 , m$

14. A stone falls from a height of $125 , m$ ($g = 9.8 , m/s^2$). Calculate the time to reach the ground.

    • (a) $4.5 , s$
    • (b) $5.0 , s$
    • (c) $5.5 , s$
    • (d) $6.0 , s$

15. A particle’s velocity changes from $8 , m/s$ to $16 , m/s$ in 2 s. What is the average acceleration?

    • (a) $2 , m/s^2$
    • (b) $3 , m/s^2$
    • (c) $4 , m/s^2$
    • (d) $5 , m/s^2$

16. A car travels 120 m in 6 s, then 80 m in 4 s in the opposite direction. Calculate the average velocity.

    • (a) $2 , m/s$
    • (b) $4 , m/s$
    • (c) $6 , m/s$
    • (d) $8 , m/s$

17. A ball is thrown upward with $u = 30 , m/s$ ($g = 9.8 , m/s^2$). Calculate the time to reach the maximum height.

    • (a) $2.5 , s$
    • (b) $3.0 , s$
    • (c) $3.5 , s$
    • (d) $4.0 , s$

18. A car decelerates from $50 , m/s$ to $30 , m/s$ in 4 s. What is the acceleration?

    • (a) $-2 , m/s^2$
    • (b) $-3 , m/s^2$
    • (c) $-4 , m/s^2$
    • (d) $-5 , m/s^2$

19. A stone is dropped from a height of $5 , m$ ($g = 9.8 , m/s^2$). What is the velocity just before hitting the ground?

    • (a) $9 , m/s$
    • (b) $10 , m/s$
    • (c) $11 , m/s$
    • (d) $12 , m/s$

20. A particle starts from rest and accelerates at $3 , m/s^2$ for 4 s. Calculate the displacement.

    • (a) $20 , m$
    • (b) $24 , m$
    • (c) $28 , m$
    • (d) $32 , m$

21. A car moves with constant velocity of $8 , m/s$ for 20 s. What is the distance traveled?

    • (a) $140 , m$
    • (b) $160 , m$
    • (c) $180 , m$
    • (d) $200 , m$

22. A ball is thrown upward with $u = 35 , m/s$ ($g = 9.8 , m/s^2$). What is the maximum height reached?

    • (a) $60 , m$
    • (b) $62 , m$
    • (c) $64 , m$
    • (d) $66 , m$

23. A car accelerates from rest at $4 , m/s^2$ for 5 s, then decelerates at $-2 , m/s^2$ for 2 s. What is the final velocity?

    • (a) $12 , m/s$
    • (b) $14 , m/s$
    • (c) $16 , m/s$
    • (d) $18 , m/s$

24. A stone falls from a height of $320 , m$ ($g = 9.8 , m/s^2$). Calculate the time to reach the ground.

    • (a) $7.5 , s$
    • (b) $8.0 , s$
    • (c) $8.5 , s$
    • (d) $9.0 , s$

25. A particle’s velocity changes from $5 , m/s$ to $15 , m/s$ in 2 s. What is the average acceleration?

    • (a) $2.5 , m/s^2$
    • (b) $3.0 , m/s^2$
    • (c) $3.5 , m/s^2$
    • (d) $4.0 , m/s^2$

26. A car travels 90 m in 5 s, then 60 m in 5 s in the same direction. Calculate the average velocity.

    • (a) $12 , m/s$
    • (b) $15 , m/s$
    • (c) $18 , m/s$
    • (d) $20 , m/s$

27. A ball is thrown upward with $u = 40 , m/s$ ($g = 9.8 , m/s^2$). Calculate the time to reach the maximum height.

    • (a) $3.5 , s$
    • (b) $4.0 , s$
    • (c) $4.5 , s$
    • (d) $5.0 , s$

28. A car decelerates from $60 , m/s$ to $40 , m/s$ in 4 s. What is the acceleration?

    • (a) $-2 , m/s^2$
    • (b) $-3 , m/s^2$
    • (c) $-4 , m/s^2$
    • (d) $-5 , m/s^2$

29. A stone is dropped from a height of $5 , m$ ($g = 9.8 , m/s^2$). What is the velocity just before hitting the ground?

    • (a) $9 , m/s$
    • (b) $10 , m/s$
    • (c) $11 , m/s$
    • (d) $12 , m/s$

30. A particle starts from rest and accelerates at $3 , m/s^2$ for 4 s. Calculate the displacement.

    • (a) $20 , m$
    • (b) $24 , m$
    • (c) $28 , m$
    • (d) $32 , m$

31. A car moves with constant velocity of $8 , m/s$ for 20 s. What is the distance traveled?

    • (a) $140 , m$
    • (b) $160 , m$
    • (c) $180 , m$
    • (d) $200 , m$

32. A ball is thrown upward with $u = 35 , m/s$ ($g = 9.8 , m/s^2$). What is the maximum height reached?

    • (a) $60 , m$
    • (b) $62 , m$
    • (c) $64 , m$
    • (d) $66 , m$

33. A car accelerates from rest at $4 , m/s^2$ for 5 s, then decelerates at $-2 , m/s^2$ for 2 s. What is the final velocity?

    • (a) $12 , m/s$
    • (b) $14 , m/s$
    • (c) $16 , m/s$
    • (d) $18 , m/s$

34. A stone falls from a height of $320 , m$ ($g = 9.8 , m/s^2$). Calculate the time to reach the ground.

    • (a) $7.5 , s$
    • (b) $8.0 , s$
    • (c) $8.5 , s$
    • (d) $9.0 , s$

35. A particle’s velocity changes from $5 , m/s$ to $15 , m/s$ in 2 s. What is the average acceleration?

    • (a) $2.5 , m/s^2$
    • (b) $3.0 , m/s^2$
    • (c) $3.5 , m/s^2$
    • (d) $4.0 , m/s^2$

Conceptual Problems

36. What is the difference between displacement and distance?

• (a) Displacement is a scalar, distance is a vector
• (b) Displacement is a vector, distance is a scalar
• (c) Both are scalars
• (d) Both are vectors

37. What does a negative acceleration indicate?

• (a) Speeding up
• (b) Slowing down or opposite direction
• (c) Constant velocity
• (d) Zero velocity

38. Which kinematic equation relates velocity, acceleration, and displacement without time?

• (a) $v = u + at$
• (b) $x = ut + \frac{1}{2} at^2$
• (c) $v^2 = u^2 + 2ax$
• (d) $x = \frac{1}{2}(u + v)t$

39. In free fall, what is the acceleration of an object near Earth’s surface?

• (a) $0 , m/s^2$
• (b) $9.8 , m/s^2$ downward
• (c) $9.8 , m/s^2$ upward
• (d) Depends on the object’s mass

40. What is the unit of instantaneous velocity?

• (a) $m$
• (b) $m/s$
• (c) $m/s^2$
• (d) $s$

41. When does average velocity equal instantaneous velocity?

• (a) When acceleration is constant
• (b) When velocity is constant
• (c) When displacement is zero
• (d) When time is zero

42. What does a zero acceleration imply?

• (a) Zero velocity
• (b) Constant velocity
• (c) Zero displacement
• (d) Changing direction

43. What is the role of initial velocity in kinematic equations?

• (a) Always zero
• (b) Velocity at $t = 0$
• (c) Final velocity
• (d) Average velocity

44. Why is acceleration constant in free fall near Earth’s surface?

• (a) Due to constant velocity
• (b) Due to constant gravity
• (c) Due to air resistance
• (d) Due to mass of the object

45. What is the dimension of acceleration?

• (a) $[\text{L} \text{T}^{-1}]$
• (b) $[\text{L} \text{T}^{-2}]$
• (c) $[\text{M} \text{L} \text{T}^{-2}]$
• (d) $[\text{L}^2 \text{T}^{-2}]$

46. How does displacement differ from distance in a round trip?

• (a) Displacement is zero, distance is zero
• (b) Displacement is zero, distance is non-zero
• (c) Displacement is non-zero, distance is zero
• (d) Both are non-zero

47. What happens to velocity when acceleration is in the opposite direction?

• (a) Increases
• (b) Decreases
• (c) Remains constant
• (d) Becomes zero

48. Which quantity is a vector in kinematics?

• (a) Distance
• (b) Speed
• (c) Velocity
• (d) Time

49. What is the significance of the kinematic equation $v^2 = u^2 + 2ax$?

• (a) Relates velocity and time
• (b) Relates displacement and time
• (c) Relates velocity and displacement without time
• (d) Relates acceleration and time

50. In free fall, what is the velocity at the maximum height of an upward-thrown object?

• (a) Zero
• (b) Equal to initial velocity
• (c) Equal to $g$
• (d) Negative

Derivation Problems

51. Derive the kinematic equation $v = u + at$ using the definition of acceleration.

52. Derive the kinematic equation $x = ut + \frac{1}{2} at^2$ by integrating velocity.

53. Derive the kinematic equation $v^2 = u^2 + 2ax$ using the other two equations.

54. Derive the average velocity formula $v_{\text{avg}} = \frac{1}{2}(u + v)$ for constant acceleration.

55. Derive the displacement of a particle in free fall starting from rest.

56. Derive the dimension of velocity using base SI units.

57. Derive the time to reach maximum height for an object thrown upward under gravity.

58. Derive the dimension of acceleration using base SI units.

59. Derive the maximum height reached by an object thrown upward under gravity.

60. Derive the displacement of a particle with constant acceleration using $v = u + at$ and $v_{\text{avg}}$.

61. Derive the velocity-time relationship for an object in free fall starting from rest.

62. Derive the position-time relationship for a particle with constant velocity.

63. Derive the displacement of a particle given $v(t) = 2t + 3$ from $t = 0$ to $t = 2$.

64. Derive the acceleration of a particle given $x(t) = 3t^2 - 4t + 1$ at $t = 1$.

65. Derive the total displacement of a particle that accelerates from rest at $2 , m/s^2$ for 3 s, then decelerates at $-1 , m/s^2$ for 2 s.

NEET-style Conceptual Problems

66. What is the unit of displacement in SI units?

• (a) $m/s$
• (b) $m$
• (c) $m/s^2$
• (d) $s$

67. What does a positive velocity and negative acceleration indicate?

• (a) Speeding up
• (b) Slowing down
• (c) Constant speed
• (d) Zero speed

68. Which of the following is a scalar quantity?

• (a) Displacement
• (b) Velocity
• (c) Acceleration
• (d) Distance

69. What is the acceleration of an object in free fall near Earth’s surface?

• (a) $0 , m/s^2$
• (b) $9.8 , m/s^2$ downward
• (c) $9.8 , m/s^2$ upward
• (d) Depends on the object’s mass

70. What is the dimension of velocity?

• (a) $[\text{L} \text{T}^{-1}]$
• (b) $[\text{L} \text{T}]$
• (c) $[\text{M} \text{L} \text{T}^{-1}]$
• (d) $[\text{L}^2 \text{T}^{-1}]$

71. What does instantaneous velocity represent?

• (a) Average velocity over a time interval
• (b) Velocity at a specific moment
• (c) Total displacement
• (d) Constant velocity

72. What is the role of the kinematic equation $x = ut + \frac{1}{2} at^2$?

• (a) Relates velocity and time
• (b) Relates displacement and time
• (c) Relates velocity and displacement
• (d) Relates acceleration and displacement

73. What happens to an object’s velocity at the maximum height when thrown upward?

• (a) It is zero
• (b) It equals initial velocity
• (c) It equals $g$
• (d) It is negative

74. Why is displacement zero in a round trip?

• (a) Distance is zero
• (b) Velocity is zero
• (c) Initial and final positions are the same
• (d) Acceleration is zero

75. What is the unit of acceleration in SI units?

• (a) $m$
• (b) $m/s$
• (c) $m/s^2$
• (d) $s$

76. What does a constant velocity imply?

• (a) Zero acceleration
• (b) Constant acceleration
• (c) Zero displacement
• (d) Changing direction

77. Which kinematic equation does not involve initial velocity?

• (a) $v = u + at$
• (b) $x = ut + \frac{1}{2} at^2$
• (c) $v^2 = u^2 + 2ax$
• (d) $x = \frac{1}{2}(u + v)t$

78. What is the acceleration of a ball thrown upward at its maximum height?

• (a) $0 , m/s^2$
• (b) $9.8 , m/s^2$ upward
• (c) $9.8 , m/s^2$ downward
• (d) Depends on the initial velocity

79. What is the dimension of displacement?

• (a) $[\text{L}]$
• (b) $[\text{L} \text{T}^{-1}]$
• (c) $[\text{L} \text{T}^{-2}]$
• (d) $[\text{M} \text{L}]$

80. What does average acceleration measure?

• (a) Change in velocity over time
• (b) Change in displacement over time
• (c) Instantaneous velocity
• (d) Constant velocity

81. Why does an object in free fall have constant acceleration?

• (a) Due to constant velocity
• (b) Due to constant gravity
• (c) Due to air resistance
• (d) Due to mass of the object

82. What is the role of the kinematic equation $v^2 = u^2 + 2ax$?

• (a) Relates velocity and time
• (b) Relates displacement and time
• (c) Relates velocity and displacement without time
• (d) Relates acceleration and time

83. What happens to velocity when acceleration is zero?

• (a) It increases
• (b) It decreases
• (c) It remains constant
• (d) It becomes negative

84. Which quantity is a vector in kinematics?

• (a) Distance
• (b) Speed
• (c) Acceleration
• (d) Time

85. What does a negative displacement indicate?

• (a) Motion in the positive direction
• (b) Motion in the negative direction
• (c) Zero velocity
• (d) Constant acceleration

86. What is the unit of average velocity?

• (a) $m$
• (b) $m/s$
• (c) $m/s^2$
• (d) $s$

87. What does instantaneous acceleration represent?

• (a) Average acceleration over a time interval
• (b) Acceleration at a specific moment
• (c) Total velocity change
• (d) Constant acceleration

88. Why is displacement a vector quantity?

• (a) It has magnitude only
• (b) It has direction only
• (c) It has both magnitude and direction
• (d) It has neither magnitude nor direction

89. What is the acceleration of an object thrown upward at its maximum height?

• (a) $0 , m/s^2$
• (b) $9.8 , m/s^2$ upward
• (c) $9.8 , m/s^2$ downward
• (d) Depends on the initial velocity

90. What does a constant acceleration imply?

• (a) Constant velocity
• (b) Linear change in velocity
• (c) Zero velocity
• (d) Changing direction

91. Which kinematic equation involves both initial and final velocities?

• (a) $v = u + at$
• (b) $x = ut + \frac{1}{2} at^2$
• (c) $v^2 = u^2 + 2ax$
• (d) $x = \frac{1}{2}(u + v)t$

92. What is the role of gravity in free fall?

• (a) Causes constant velocity
• (b) Causes constant acceleration
• (c) Causes zero acceleration
• (d) Causes changing acceleration

93. What does a positive velocity and positive acceleration indicate?

• (a) Speeding up
• (b) Slowing down
• (c) Constant speed
• (d) Zero speed

94. What is the dimension of average acceleration?

• (a) $[\text{L} \text{T}^{-1}]$
• (b) $[\text{L} \text{T}^{-2}]$
• (c) $[\text{M} \text{L} \text{T}^{-2}]$
• (d) $[\text{L}^2 \text{T}^{-2}]$

95. Why is distance always positive?

• (a) It is a vector quantity
• (b) It is a scalar quantity
• (c) It depends on direction
• (d) It depends on acceleration

NEET-style Numerical Problems

96. A car starts from rest and accelerates at $2 , m/s^2$ for 5 s. What is the final velocity?

• (a) $8 , m/s$
• (b) $10 , m/s$
• (c) $12 , m/s$
• (d) $14 , m/s$

97. A ball is dropped from a height of $10 , m$ ($g = 9.8 , m/s^2$). What is the time to reach the ground?

• (a) $1.2 , s$
• (b) $1.4 , s$
• (c) $1.6 , s$
• (d) $1.8 , s$

98. A particle moves 60 m in 4 s, then 40 m in 2 s in the same direction. What is the average velocity?

• (a) $14 , m/s$
• (b) $16.7 , m/s$
• (c) $18 , m/s$
• (d) $20 , m/s$

99. A ball is thrown upward with $u = 15 , m/s$ ($g = 9.8 , m/s^2$). What is the maximum height reached?

• (a) $10 , m$
• (b) $11 , m$
• (c) $12 , m$
• (d) $13 , m$

100. A car decelerates from $45 , m/s$ to $25 , m/s$ in 5 s. What is the acceleration?
     - (a) $-2 , m/s^2$
     - (b) $-3 , m/s^2$
     - (c) $-4 , m/s^2$
     - (d) $-5 , m/s^2$

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