Worksheet: Kinetic Energy

In this worksheet, we will practice calculating the kinetic energy of a moving particle of mass m that moves with velocity v.

Q1:

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

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

Q2:

A body of mass 500 g is moving at a constant velocity v i j = ( 2 3 ) / c m s , where i and j are two perpendicular unit vectors. Find its kinetic energy.

  • A 1,250 ergs
  • B 3 . 2 5 × 1 0 ergs
  • C 3,250 ergs
  • D 6 . 5 × 1 0 ergs
  • E 6,500 ergs

Q3:

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.

Q4:

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.

Q5:

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 .

Q6:

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 469.41 joules
  • C 12.93 joules
  • D 319.07 joules
  • E 159.54 joules

Q7:

A body of mass 8 kg was projected vertically upwards 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 .

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

Q8:

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 3 7 . Taking 𝑔 = 9 . 8 / m s , determine the change in the body’s kinetic energy in the first 5 seconds of motion.

Q9:

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

Q10:

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 .

Q11:

A train of mass 56 metric tons 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 joules
  • B 1 . 4 5 × 1 0 joules
  • C 7 . 1 7 × 1 0 joules
  • D 1 . 1 2 × 1 0 joules
  • E 2 . 2 4 × 1 0 joules

Q12:

A body is moving at a constant velocity v i j = ( 2 5 0 2 5 0 ) / c m s , where i and j are two perpendicular unit vectors. Given that the kinetic energy of the body is 4.8 joules, find the mass of the body.

Q13:

A particle is moving in a straight line. At time 𝑡 seconds, where 𝑡 0 , the particle’s displacement relative to a fixed point is given by s i j = 2 𝑡 + 8 𝑡 ( 1 0 𝑡 ) m , where i and j are two perpendicular unit vectors. Given that the kinetic energy of the body at 𝑡 = 7 s is 30 joules, determine the body’s mass.

Q14:

A body of mass 1 kg is moving in a straight line. After time 𝑡 seconds, where 𝑡 0 , the body’s displacement relative to a fixed point is given by s e = 6 𝑡 2 𝑡 m , where e is a fixed unit vector. Find the kinetic energy of the body, 3 seconds after it started moving.

Q15:

A body of mass 3 kg is moving across a plane. At time 𝑡 seconds, where 𝑡 0 , the body’s position vector relative to a fixed point is given by r e = 𝑎 𝑡 + 6 𝑡 + 2 m , where e is a fixed unit vector. Given that at 𝑡 = 3 s , the kinetic energy of the body is 54 joules, find all the possible values of 𝑎 .

  • A 𝑎 = 2
  • B 𝑎 = 1
  • C 𝑎 = 2 or 𝑎 = 0
  • D 𝑎 = 4 or 𝑎 = 0

Q16:

A body of mass 2 kg is moving under the action of three forces: F i j = ( 8 + 2 ) N , F i j = ( 1 0 + 4 ) N , and F i j = ( 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 m . Find the body’s kinetic energy 2 seconds after the forces started acting.

Q17:

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

Q18:

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 .

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

Q19:

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 .

Q20:

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 5.05 m
  • C 4.9 m
  • D 4.59 m

Q21:

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

Q22:

A sphere 𝐴 of mass 1.5 kg was moving at 10.4 m/s across a horizontal plane. It collided with another sphere 𝐵 of mass 2 kg that had been at rest on the same plane. Given that the ratio between their respective speeds after collision was 5 6 , find the loss in the kinetic energy as a result of the impact.

Q23:

A body was at rest on a horizontal plane. A horizontal force acted on it until its momentum became 88,200 dyn⋅s, and its kinetic energy became 20,250 g-wt⋅cm. At that moment, the force stopped acting, and the body traveled a further 18 m before it came to rest. Find the mass of the body and the resistance of the plane 𝑅 assuming that it was constant. Take 𝑔 = 9 . 8 / m s

  • A 𝑚 = 3 9 2 g , 𝑅 = 4 4 , 1 0 0 d y n e s
  • B 𝑚 = 1 9 6 g , 𝑅 = 2 2 , 0 5 0 d y n e s
  • C 𝑚 = 1 9 6 g , 𝑅 = 1 1 , 0 2 5 d y n e s
  • D 𝑚 = 3 9 2 g , 𝑅 = 2 2 , 0 5 0 d y n e s

Q24:

A mechanical hammer of mass 912 kg was raised to a height of 6.4 m before being released to fall vertically on a pole of mass 304 kg and push it into the ground. Find the kinetic energy lost due to the collision. Take 𝑔 = 9 . 8 / m s .

  • A 76,267.52 joules
  • B 57,200.64 joules
  • C 14,300.16 joules
  • D 42,900.48 joules

Q25:

A particle of mass 225 g started moving from the top of a smooth plane inclined to the horizontal at an angle whose sine is 1 3 . Given that the plane was 48 m long, find the kinetic energy of the particle when it reached the bottom of the plane. Take 𝑔 = 9 . 8 / m s .

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