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Worksheet: Kinetic Energy

Q1:

A particle of mass 150 g was projected at 13 m/s across a horizontal plane. It decelerated uniformly at 2 m/s2. Find the change in its kinetic energy in the first 4 seconds of motion.

Q2:

A rubber ball of mass 125 g fell vertically from a height of 3.6 m. It hit the ground and rebounded vertically upward. Given that the change in the ball’s momentum as a result of the impact was 1 . 9 × 1 0 5 g⋅cm/s, determine the change in its kinetic energy. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 3 . 0 4 × 1 0 8 erg
  • B 1 . 5 2 × 1 0 7 erg
  • C 3 . 0 4 × 1 0 8 erg
  • D 1 . 5 2 × 1 0 7 erg

Q3:

A body of mass 500 g is moving at a constant velocity , where and are two perpendicular unit vectors. Find its kinetic energy.

  • A
    1 250
    ergs
  • B
    6 500
    ergs
  • C ergs
  • D
    3 250
    ergs
  • E ergs

Q4:

A body is moving at a constant velocity , where and are two perpendicular unit vectors. Given that the kinetic energy of the body is 4.8 joules, find the mass of the body.

Q5:

A cannon fired a shell of mass 16 kg at 285 m/s towards a tank that was moving at 72 km/h in a straight line directly towards the cannon. Determine the kinetic energy of the shell relative to the motion of the tank.

Q6:

A particle is moving in a straight line. At time seconds, where , the particle’s displacement relative to a fixed point is given by , where and are two perpendicular unit vectors. Given that the kinetic energy of the body at is 30 joules, determine the body’s mass.

Q7:

A train of mass 56 tonnes was moving on a straight section of horizontal track. The resistance to the train’s motion was proportional to the square of its speed. Given that the force generated by the train’s engine was 700 kg-wt, and the resistance to its motion was 8 kg-wt per tonne of its mass when its speed was 57.6 km/h, determine the train’s maximum possible kinetic energy.

  • A 1 . 4 5 × 1 0 8 joules
  • B 2 . 2 4 × 1 0 7 joules
  • C 7 . 1 7 × 1 0 6 joules
  • D 1 . 1 2 × 1 0 7 joules
  • E 1 . 4 5 × 1 0 7 joules

Q8:

A ball of mass 100 g fell vertically from a height of 7 m onto a section of horizontal ground. The ball hit the ground and rebounded vertically upward. The loss of kinetic energy as a result of the collision was 1.568 joules. Determine the maximum height the ball reached after the first bounce. Consider the acceleration due to gravity to be 𝑔 = 9 . 8 / m s 2 .

  • A 6.2 m
  • B 1.6 m
  • C 3.8 m
  • D 5.4 m

Q9:

A body of mass 1.7 kg is projected vertically upward at 13.7 m/s from the surface of the Earth. Find its kinetic energy 1 second after it was projected. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 25.86 joules
  • B 159.54 joules
  • C 319.07 joules
  • D 12.93 joules
  • E 469.41 joules

Q10:

A ball of mass 50 g fell vertically from a height of 6 m above the surface of the ground. It rebounded vertically upward to a height of 3 m before it momentarily came to rest. Determine the change in its kinetic energy due to the impact. Take 𝑔 = 9 . 8 / m s 2 .

  • A 1.47 joules
  • B 2 . 9 4 joules
  • C 2.94 joules
  • D 1 . 4 7 joules

Q11:

A body of mass 28 kg was moving at 28 m/s when a force started acting on it. As a result, its speed became 7 m/s. Find the change in kinetic energy of the body. Take .

Q12:

A particle of mass 500 g fell vertically from a height of 17.6 m above the ground. Determine its kinetic energy just before it hit the ground. Consider the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

Q13:

A body of mass 3 kg is moving across a plane. At time seconds, where , the body’s position vector relative to a fixed point is given by , where is a fixed unit vector. Given that at , the kinetic energy of the body is 54 joules, find all the possible values of .

  • A
  • B
  • C or
  • D or

Q14:

A body of mass 2 kg is moving under the action of three forces: F i j 1 = ( 8 + 2 ) N , F i j 2 = ( 1 0 + 4 ) N , and F i j 3 = ( 2 1 0 ) N , where i and j are two perpendicular unit vectors. After time 𝑡 seconds, where 𝑡 0 , the body’s displacement relative to a fixed point is given by s i j = 𝑎 𝑡 𝑏 𝑡 𝑡 2 2 m . Find the body’s kinetic energy 2 seconds after the forces started acting.

Q15:

A sphere of mass 850 g fell vertically from a height of 5.2 m onto a horizontal section of ground. It rebounded vertically upward. Given that the acceleration due to gravity is 9.8 m/s2 and the loss in the sphere’s kinetic energy as a result of the collision was 2.54, determine the maximum height the sphere reached after impact.

  • A 5.51 m
  • B 4.59 m
  • C 5.05 m
  • D 4.9 m

Q16:

A body of mass 1 kg is moving in a straight line. After time seconds, where , the body’s displacement relative to a fixed point is given by , where is a fixed unit vector. Find the kinetic energy of the body, 3 seconds after it started moving.

Q17:

Given that the kinetic energy of a moving bullet of mass 1 3 5 kg, at a certain instant, was 7 000 joules, determine its speed.

Q18:

A ball fell vertically from the top of a tower. Just before it struck the ground, its momentum was 882 g⋅m/s, and its kinetic energy was 1 512 g-wt⋅m. Calculate the mass of the body 𝑚 and the height of the tower . Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 𝑚 = 1 0 5 g , = 1 8 m
  • B 𝑚 = 5 2 . 5 g , = 1 4 . 4 m
  • C 𝑚 = 2 1 0 g , = 6 . 3 m
  • D 𝑚 = 2 6 . 2 5 g , = 5 7 . 6 m

Q19:

A force of 150 g-wt was acting on a body of mass 189 g that was resting on a smooth horizontal plane. Determine the body’s kinetic energy 6 seconds after the force started acting on it. Take 𝑔 = 9 . 8 / m s 2 .

Q20:

A body was at rest on a horizontal plane. A force of 26.25 g-wt acted on the body until its momentum became 55 566 g⋅cm/s, at which point its kinetic energy was 5 670 g-wt⋅cm. After the force stopped acting, the body continued moving for another 5.4 m until it came to rest. Find the mass of the body 𝑚 , and determine the time 𝑡 , in seconds, that the force acted for. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 𝑚 = 5 5 5 . 6 6 g , 𝑡 = 3 . 6 s
  • B 𝑚 = 2 7 7 . 8 3 g , 𝑡 = 2 . 1 6 s
  • C 𝑚 = 5 5 5 . 6 6 g , 𝑡 = 2 . 1 6 s
  • D 𝑚 = 2 7 7 . 8 3 g , 𝑡 = 3 . 6 s

Q21:

A body of mass 1 kg was projected at 2 m/s up the line greatest slope of a smooth plane inclined to the horizontal at an angle whose sine is . Taking , determine the change in the body’s kinetic energy in the first 5 seconds of motion.

Q22:

A body of mass 750 g was projected at 450 cm/s up the line of greatest slope of a smooth plane inclined at 3 0 to the horizontal. Find its kinetic energy 4 seconds after it was projected.

  • A 1 . 4 4 1 × 1 0 9 ergs
  • B 1 . 7 1 × 1 0 9 ergs
  • C 7 . 5 9 4 × 1 0 7 ergs
  • D 8 . 5 5 × 1 0 8 ergs
  • E 2 . 1 7 8 × 1 0 9 ergs

Q23:

A smooth plane is inclined at an angle 𝜃 to the horizontal, where s i n 𝜃 = 1 1 0 . A body of mass 8 kg is projected at 15 m/s up a line of greatest slope of a plane. Determine the change in the body’s kinetic energy in the first 5 seconds of its motion. Take 𝑔 = 9 . 8 / m s 2 .

Q24:

A body of mass 8 kg was projected vertically upward at 34.3 m/s. After a certain time 𝑡 , its kinetic energy became 198.45 joules. Find 𝑡 . Take 𝑔 = 9 . 8 / m s 2 .

  • A 𝑡 = 0 . 6 2 5 s or 𝑡 = 2 . 8 7 5 s
  • B 𝑡 = 1 . 2 5 s or 𝑡 = 0 . 6 2 5 s
  • C 𝑡 = 2 . 5 s
  • D 𝑡 = 1 . 2 5 s or 𝑡 = 5 . 7 5 s

Q25:

Find the kinetic energy of a body of mass 4 kg moving at 36 m/s. Express your answer in ergs.

  • A 1 . 0 3 7 × 1 0 1 1 erg
  • B 5 . 1 8 4 × 1 0 1 0 erg
  • C 2 592 erg
  • D 2 . 5 9 2 × 1 0 1 0 erg
  • E 2 . 5 9 2 × 1 0 6 erg