Kinetic Energy and Work Problems

This section provides 100 problems to test your understanding of kinetic energy and work, including the definition of work, kinetic energy and the work-energy theorem, work done by variable forces (e.g., springs), and power in mechanical systems. 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 in mastering energy concepts, a key topic for JEE/NEET success.

Numerical Problems

1. A $5kg$ block on a frictionless surface is pushed by $F=20N$ over $d=4m$ at $\theta =0^{\circ }$. Calculate the work done by the force.

   • (a) $60J$
   • (b) $80J$
   • (c) $100J$
   • (d) $120J$

2. A $2kg$ block on a frictionless incline at ${30}^{\circ }$ slides $d=3m$ ($g=9.8m/s^2$). Calculate the work done by gravity.

   • (a) $25.0J$
   • (b) $29.4J$
   • (c) $33.8J$
   • (d) $38.2J$

3. A $3kg$ block initially at rest on a frictionless surface is pushed by $F=15N$ over $d=6m$. Calculate the final speed.

   • (a) $5.0m/s$
   • (b) $6.0m/s$
   • (c) $7.0m/s$
   • (d) $8.0m/s$

4. A $4kg$ block moving at $v_i=5m/s$ on a surface with ${\mu }_k=0.2$ ($g=9.8m/s^2$) travels $d=4m$. Calculate the final speed.

   • (a) $2.0m/s$
   • (b) $3.0m/s$
   • (c) $4.0m/s$
   • (d) $5.0m/s$

5. A spring with $k=300N/m$ is stretched from $x=0$ to $x=0.2m$. Calculate the work done by the spring.

   • (a) $-6.0J$
   • (b) $-5.0J$
   • (c) $-4.0J$
   • (d) $-3.0J$

6. A $1000kg$ car moving at $v=25m/s$ with $F=600N$ in the direction of motion. Calculate the power.

   • (a) $10kW$
   • (b) $12.5kW$
   • (c) $15kW$
   • (d) $17.5kW$

7. A $2kg$ block on a frictionless surface with $\overrightarrow{F}=8\hat{i}+6\hat{j}N$ is displaced $\overrightarrow{d}=3\hat{i}+2\hat{j}m$. Calculate the work done.

   • (a) $36J$
   • (b) $40J$
   • (c) $44J$
   • (d) $48J$

8. A $1kg$ block moving at $v_i=6m/s$ on a surface with ${\mu }_k=0.3$ ($g=9.8m/s^2$). Calculate the distance it travels before stopping.

   • (a) $5.0m$
   • (b) $5.5m$
   • (c) $6.0m$
   • (d) $6.5m$

9. A spring with $k=400N/m$ is compressed from $x=0$ to $x=-0.15m$. Calculate the work done to compress the spring.

   • (a) $4.0J$
   • (b) $4.5J$
   • (c) $5.0J$
   • (d) $5.5J$

10. A $500W$ pump lifts water at $v=2.5m/s$ ($g=9.8m/s^2$). Calculate the mass flow rate.

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

11. A $4kg$ block on a frictionless surface is pushed by $F=12N$ at ${60}^{\circ }$ over $d=5m$. Calculate the work done by the force.

    • (a) $25J$
    • (b) $30J$
    • (c) $35J$
    • (d) $40J$

12. A $5kg$ block moving at $v_i=8m/s$ on a surface with ${\mu }_k=0.1$ ($g=9.8m/s^2$) travels $d=10m$. Calculate the final speed.

    • (a) $6.0m/s$
    • (b) $7.0m/s$
    • (c) $8.0m/s$
    • (d) $9.0m/s$

13. A $0.5kg$ mass on a spring ($k=200N/m$) is released from $x=0.3m$. Calculate the speed at $x=0$.

    • (a) $5.0m/s$
    • (b) $6.0m/s$
    • (c) $7.0m/s$
    • (d) $8.0m/s$

14. A person lifts a $15kg$ mass at $v=0.4m/s$ ($g=9.8m/s^2$). Calculate the power.

    • (a) $50W$
    • (b) $55W$
    • (c) $60W$
    • (d) $65W$

15. A $3kg$ block on a frictionless incline at ${37}^{\circ }$ slides $d=2m$ ($g=9.8m/s^2$). Calculate the work done by gravity.

    • (a) $30.0J$
    • (b) $35.3J$
    • (c) $40.6J$
    • (d) $45.9J$

16. A $2kg$ block initially at rest on a frictionless surface is pushed by $F=8N$ over $d=4m$. Calculate the final speed.

    • (a) $4.0m/s$
    • (b) $5.0m/s$
    • (c) $6.0m/s$
    • (d) $7.0m/s$

17. A force $F(x)=4x+2$ acts from $x=0$ to $x=3m$. Calculate the work done.

    • (a) $15J$
    • (b) $18J$
    • (c) $21J$
    • (d) $24J$

18. A $1000kg$ car moving at $v=15m/s$ with $F=400N$ at ${45}^{\circ }$ to the motion. Calculate the power by the force.

    • (a) $4.0kW$
    • (b) $4.2kW$
    • (c) $4.5kW$
    • (d) $4.8kW$

19. A $6kg$ block moving at $v_i=10m/s$ on a surface with ${\mu }_k=0.25$ ($g=9.8m/s^2$). Calculate the distance it travels before stopping.

    • (a) $15.0m$
    • (b) $17.5m$
    • (c) $20.0m$
    • (d) $22.5m$

20. A spring with $k=500N/m$ is stretched from $x=0$ to $x=0.1m$. Calculate the work done to stretch the spring.

    • (a) $2.0J$
    • (b) $2.5J$
    • (c) $3.0J$
    • (d) $3.5J$

21. A $5kg$ block on a frictionless surface with $\overrightarrow{F}=6\hat{i}+8\hat{j}N$ is displaced $\overrightarrow{d}=4\hat{i}+3\hat{j}m$. Calculate the work done.

    • (a) $42J$
    • (b) $46J$
    • (c) $50J$
    • (d) $54J$

22. A $1kg$ mass on a spring ($k=150N/m$) is released from $x=0.25m$. Calculate the speed at $x=0.1m$.

    • (a) $2.0m/s$
    • (b) $3.0m/s$
    • (c) $4.0m/s$
    • (d) $5.0m/s$

23. A $2000kg$ truck moving at $v=30m/s$ with $F=800N$ in the direction of motion. Calculate the power.

    • (a) $20kW$
    • (b) $22kW$
    • (c) $24kW$
    • (d) $26kW$

24. A $7kg$ block moving at $v_i=12m/s$ on a surface with ${\mu }_k=0.15$ ($g=9.8m/s^2$). Calculate the distance it travels before stopping.

    • (a) $40.0m$
    • (b) $45.0m$
    • (c) $50.0m$
    • (d) $55.0m$

25. A spring with $k=600N/m$ is compressed from $x=0$ to $x=-0.2m$. Calculate the work done by the spring.

    • (a) $-12.0J$
    • (b) $-10.0J$
    • (c) $-8.0J$
    • (d) $-6.0J$

26. A $3kg$ block on a frictionless incline at ${53}^{\circ }$ slides $d=5m$ ($g=9.8m/s^2$). Calculate the work done by gravity.

    • (a) $90.0J$
    • (b) $100.0J$
    • (c) $110.0J$
    • (d) $120.0J$

27. A $2kg$ block initially at rest on a frictionless surface is pushed by $F=10N$ over $d=8m$. Calculate the final speed.

    • (a) $6.0m/s$
    • (b) $7.0m/s$
    • (c) $8.0m/s$
    • (d) $9.0m/s$

28. A force $F(x)=5x^2+3$ acts from $x=1$ to $x=4m$. Calculate the work done.

    • (a) $180J$
    • (b) $190J$
    • (c) $200J$
    • (d) $210J$

29. A $1500kg$ car moving at $v=18m/s$ with $F=300N$ at ${60}^{\circ }$ to the motion. Calculate the power by the force.

    • (a) $2.5kW$
    • (b) $2.7kW$
    • (c) $2.9kW$
    • (d) $3.1kW$

30. A $0.4kg$ mass on a spring ($k=250N/m$) is released from $x=0.4m$. Calculate the speed at $x=0$.

    • (a) $8.0m/s$
    • (b) $9.0m/s$
    • (c) $10.0m/s$
    • (d) $11.0m/s$

31. A $600W$ pump lifts water at $v=3m/s$ ($g=9.8m/s^2$). Calculate the mass flow rate.

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

32. A $8kg$ block moving at $v_i=15m/s$ on a surface with ${\mu }_k=0.2$ ($g=9.8m/s^2$). Calculate the distance it travels before stopping.

    • (a) $50.0m$
    • (b) $55.0m$
    • (c) $60.0m$
    • (d) $65.0m$

33. A spring with $k=800N/m$ is stretched from $x=0$ to $x=0.25m$. Calculate the work done to stretch the spring.

    • (a) $20.0J$
    • (b) $22.5J$
    • (c) $25.0J$
    • (d) $27.5J$

34. A person lifts a $20kg$ mass at $v=0.3m/s$ ($g=9.8m/s^2$). Calculate the power.

    • (a) $55W$
    • (b) $60W$
    • (c) $65W$
    • (d) $70W$

35. A $1kg$ block on a frictionless surface with $\overrightarrow{F}=10\hat{i}+5\hat{j}N$ is displaced $\overrightarrow{d}=3\hat{i}+6\hat{j}m$. Calculate the work done.

    • (a) $55J$
    • (b) $60J$
    • (c) $65J$
    • (d) $70J$

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Conceptual Problems

36. What does the work done by a force depend on?

• (a) Force magnitude only
• (b) Displacement magnitude only
• (c) Force, displacement, and the angle between them
• (d) Force and time

37. What does the work-energy theorem state?

• (a) Work done equals potential energy
• (b) Net work equals change in kinetic energy
• (c) Work done equals total energy
• (d) Net work equals change in potential energy

38. What is the work done by a spring when stretched?

• (a) Positive
• (b) Negative
• (c) Zero
• (d) Depends on the direction

39. What does power measure?

• (a) Total work done
• (b) Rate of work done
• (c) Total energy
• (d) Rate of energy change

40. What is the unit of kinetic energy?

• (a) $N$
• (b) $J$
• (c) $W$
• (d) $kg$

41. What happens to kinetic energy if speed doubles?

• (a) Doubles
• (b) Triples
• (c) Quadruples
• (d) Halves

42. What is the work done by a force perpendicular to displacement?

• (a) Maximum
• (b) Minimum
• (c) Zero
• (d) Negative

43. What does the work to stretch a spring depend on?

• (a) Spring constant only
• (b) Displacement only
• (c) Spring constant and displacement squared
• (d) Mass of the spring

44. How does friction affect kinetic energy?

• (a) Increases it
• (b) Decreases it
• (c) Does not affect it
• (d) Makes it zero

45. What is the dimension of power?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (b) $[\text{M}{\text{L}}^2{\text{T}}^{-3}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}\text{L}{\text{T}}^{-3}]$

46. What does a negative work imply?

• (a) Force aids displacement
• (b) Force opposes displacement
• (c) No displacement
• (d) No force

47. What is the significance of $\frac{1}{2}m{v}^2$?

• (a) Potential energy
• (b) Kinetic energy
• (c) Work done
• (d) Power

48. What is the physical significance of power in lifting?

• (a) Total work done
• (b) Rate of energy transfer
• (c) Total energy
• (d) Acceleration

49. What does the work-energy theorem simplify?

• (a) Force calculations
• (b) Motion problems without force details
• (c) Potential energy calculations
• (d) Power calculations

50. How does the angle between force and displacement affect work?

• (a) No effect
• (b) Determines the sign and magnitude
• (c) Only affects the sign
• (d) Only affects the magnitude

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Derivation Problems

51. Derive the work done by a constant force in 2D.

52. Derive the work done by gravity on an incline.

53. Derive the work-energy theorem for a constant force.

54. Derive the work done by a spring force.

55. Derive the power for a constant force.

56. Derive the work done by a variable force in 1D.

57. Derive the speed of a mass on a spring at a given position.

58. Derive the distance to stop a block with friction using the work-energy theorem.

59. Derive the work-energy theorem for a general path.

60. Derive the mass flow rate from power in a lifting system.

61. Derive the work done by friction on an incline.

62. Derive the power in a system with friction and constant speed.

63. Derive the final speed of a block under a variable force.

64. Derive the work done by a force at an angle.

65. Derive the kinetic energy change in a 2D motion problem.

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NEET-style Conceptual Problems

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

• (a) $N$
• (b) $J$
• (c) $W$
• (d) $kg$

67. What does a zero work imply?

• (a) Force is zero
• (b) Displacement is zero
• (c) Force is perpendicular to displacement
• (d) All of the above

68. Which quantity is a scalar in work calculations?

• (a) Force
• (b) Displacement
• (c) Work
• (d) Velocity

69. What happens to kinetic energy if mass doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Remains the same

70. What is the dimension of kinetic energy?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (b) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-3}]$

71. What does the work-energy theorem relate?

• (a) Work to potential energy
• (b) Net work to change in kinetic energy
• (c) Work to power
• (d) Net work to change in potential energy

72. What is the role of the spring constant in work calculations?

• (a) Determines force magnitude
• (b) Determines work magnitude
• (c) Determines energy stored
• (d) Determines displacement

73. What happens to power if velocity doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Remains the same

74. Why does friction do negative work?

• (a) It acts in the direction of motion
• (b) It acts opposite to the direction of motion
• (c) It acts perpendicular to motion
• (d) It acts along the normal force

75. What is the unit of power?

• (a) $J$
• (b) $W$
• (c) $N$
• (d) $kg$

76. What does a constant speed imply in work-energy problems?

• (a) Zero net work
• (b) Positive net work
• (c) Negative net work
• (d) Constant acceleration

77. Which force does no work in circular motion?

• (a) Centripetal force
• (b) Frictional force
• (c) Gravitational force
• (d) Tension force

78. What is the direction of work done by gravity?

• (a) Always downward
• (b) Along the displacement
• (c) Perpendicular to displacement
• (d) Opposite to displacement

79. What does a pseudo-force do in a non-inertial frame?

• (a) Increases work
• (b) Affects net work calculations
• (c) Provides centripetal force
• (d) Reduces friction

80. What is the dimension of work?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (b) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-3}]$

81. What is the role of kinetic energy in motion?

• (a) Measures potential energy
• (b) Measures energy of motion
• (c) Measures work done
• (d) Measures power

82. What happens to the work done by a spring when it returns to equilibrium?

• (a) Positive
• (b) Negative
• (c) Zero
• (d) Depends on the direction

83. Why does power depend on velocity?

• (a) Velocity determines force
• (b) Velocity determines work
• (c) Velocity determines the rate of work
• (d) Velocity determines displacement

84. What does a positive work imply?

• (a) Force opposes displacement
• (b) Force aids displacement
• (c) No displacement
• (d) No force

85. What is the unit of the spring constant?

• (a) $N/m$
• (b) $J$
• (c) $W$
• (d) $kg$

86. What does a zero kinetic energy imply?

• (a) Object is moving
• (b) Object is at rest
• (c) Object is accelerating
• (d) Object is in circular motion

87. What is the physical significance of $\overrightarrow{F}\cdot \overrightarrow{v}$?

• (a) Work
• (b) Kinetic energy
• (c) Power
• (d) Potential energy

88. Why does gravity do work on an incline?

• (a) It acts perpendicular to motion
• (b) It has a component along displacement
• (c) It acts opposite to motion
• (d) It acts along the normal force

89. What is the dimension of the spring constant?

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

90. How does friction affect the work-energy theorem?

• (a) Increases kinetic energy
• (b) Decreases kinetic energy
• (c) Does not affect kinetic energy
• (d) Increases potential energy

91. What is the role of work in energy transfer?

• (a) Measures kinetic energy
• (b) Transfers energy due to force
• (c) Measures potential energy
• (d) Measures power

92. What does a zero power indicate?

• (a) No work done over time
• (b) No force applied
• (c) No velocity
• (d) Both (a) and (c)

93. What is the physical significance of $\frac{1}{2}k{x}^2$?

• (a) Kinetic energy
• (b) Work done by a spring
• (c) Work to stretch a spring
• (d) Power

94. What is the dimension of mass flow rate?

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

95. Why does the work-energy theorem simplify motion problems?

• (a) Avoids force calculations
• (b) Avoids energy calculations
• (c) Avoids velocity calculations
• (d) Avoids displacement calculations

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NEET-style Numerical Problems

96. A $4kg$ block on a frictionless surface is pushed by $F=16N$ over $d=5m$. What is the work done?

• (a) $70J$
• (b) $80J$
• (c) $90J$
• (d) $100J$

97. A $2kg$ block moving at $v_i=6m/s$ on a surface with ${\mu }_k=0.2$ ($g=9.8m/s^2$). What is the distance it travels before stopping?

• (a) $7.0m$
• (b) $8.0m$
• (c) $9.0m$
• (d) $10.0m$

98. A spring with $k=200N/m$ is stretched from $x=0$ to $x=0.15m$. What is the work done to stretch the spring?

• (a) $2.0J$
• (b) $2.25J$
• (c) $2.5J$
• (d) $2.75J$

99. A $1200kg$ car moving at $v=20m/s$ with $F=500N$ in the direction of motion. What is the power?

• (a) $8kW$
• (b) $9kW$
• (c) $10kW$
• (d) $11kW$

100. A $0.3kg$ mass on a spring ($k=100N/m$) is released from $x=0.2m$. What is the speed at $x=0$?
     - (a) $2.0m/s$
     - (b) $2.5m/s$
     - (c) $3.0m/s$
     - (d) $3.5m/s$

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