# 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 erg
- B erg
- C 2 592 erg
- D erg
- E 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 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 .

**Q5: **

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

**Q6: **

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.

**Q7: **

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 .

**Q8: **

A body of mass 1.7 kg is projected vertically upwards at
13.7 m/s
from the surface of the Earth. Find, to the nearest two decimal places, its kinetic energy
1 second after it was projected. Consider the acceleration due to
gravity to be 9.8 m/s^{2}.

**Q9: **

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

- A or
- B or
- C
- D or

**Q10: **

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.

**Q11: **

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

- A ergs
- B ergs
- C ergs
- D ergs
- E ergs

**Q12: **

A smooth plane is inclined at an angle to the horizontal, where . 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 .

**Q13: **

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 joules
- B joules
- C joules
- D joules
- E joules

**Q14: **

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.

**Q15: **

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.

**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: **

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

**Q18: **

A body of mass 2 kg is moving under the action of three forces: , , and , where and are two perpendicular unit vectors. After time seconds, where , the body’s displacement relative to a fixed point is given by . Find the body’s kinetic energy 2 seconds after the forces started acting.

**Q19: **

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
, and determine the time , in seconds, that
the force acted for. Consider the acceleration due to gravity to be
9.8 m/s^{2}.

- A ,
- B ,
- C ,
- D ,

**Q20: **

A rubber ball of mass 125 g fell vertically from a height
of 3.6 m. It hit the ground and rebounded vertically
upwards. Given that the change in the ball’s momentum as a result of the impact was
g⋅cm/s, determine the change in
its kinetic energy. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

- A erg
- B erg
- C erg
- D erg

**Q21: **

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 upwards. 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 .

**Q22: **

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

**Q23: **

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 .

**Q24: **

A sphere of mass 700 g fell vertically from a height of 10 m onto a horizontal section of ground. It rebounded vertically upwards. Given that the acceleration due to gravity is 9.8 m/s^{2} and the loss in the sphere’s kinetic energy as a result of the collision was 43.904, determine the maximum height the sphere reached after impact.

- A 16.4 m
- B 2.8 m
- C 6.8 m
- D 3.6 m

**Q25: **

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 and the height of the tower
. Consider the acceleration due to gravity to be
9.8 m/s^{2}.

- A ,
- B ,
- C ,
- D ,