Lesson: Kinetic Energy

In this lesson, we will learn how to calculate the kinetic energy of a moving particle of mass m that moves with velocity v.

Video

08:55

Sample Question Videos

  • 02:49

Worksheet: Kinetic Energy • 25 Questions • 1 Video

Q1:

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

Q2:

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.

Q3:

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

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 𝑔 = 9 . 8 / m s  .

Q5:

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.

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 𝑔 = 9 . 8 / m s 2 .

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/s2.

Q9:

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

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 3 7 . Taking 𝑔 = 9 . 8 / m s  , 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 3 0 ∘ to the horizontal. Find its kinetic energy 4 seconds after it was projected.

Q12:

A smooth plane is inclined at an angle πœƒ to the horizontal, where s i n πœƒ = 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 .

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.

Q14:

A body is moving at a constant velocity ⃑ 𝑣 = ο€Ί 2 5 0 ⃑ 𝑖 βˆ’ 2 5 0 ⃑ 𝑗  / 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.

Q15:

A particle is moving in a straight line. At time 𝑑 seconds, where 𝑑 β‰₯ 0 , the particle’s displacement relative to a fixed point is given by ⃑ 𝑠 =  ο€Ή βˆ’ 2 𝑑 + 8 𝑑  ⃑ 𝑖 βˆ’ ( 1 0 𝑑 ) ⃑ 𝑗  2 m , where ⃑ 𝑖 and ⃑ 𝑗 are two perpendicular unit vectors. Given that the kinetic energy of the body at 𝑑 = 7 s is 30 joules, determine the body’s mass.

Q16:

A body of mass 1 kg is moving in a straight line. After time 𝑑 seconds, where 𝑑 β‰₯ 0 , the body’s displacement relative to a fixed point is given by ⃑ 𝑠 =  ο€Ή βˆ’ 6 𝑑 βˆ’ 2 𝑑  ⃑ 𝑒  2 m , where ⃑ 𝑒 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 𝑑 seconds, where 𝑑 β‰₯ 0 , the body’s position vector relative to a fixed point is given by ⃑ π‘Ÿ =  ο€Ή π‘Ž 𝑑 + 6 𝑑 + 2  ⃑ 𝑒  2 m , where ⃑ 𝑒 is a fixed unit vector. Given that at 𝑑 = 3 s , the kinetic energy of the body is 54 joules, find all the possible values of π‘Ž .

Q18:

A body of mass 2 kg is moving under the action of three forces: ⃑ 𝐹 = ο€Ί βˆ’ 8 ⃑ 𝑖 + 2 ⃑ 𝑗  1 N , ⃑ 𝐹 = ο€Ί 1 0 ⃑ 𝑖 + 4 ⃑ 𝑗  2 N , and ⃑ 𝐹 = ο€Ί βˆ’ 2 ⃑ 𝑖 βˆ’ 1 0 ⃑ 𝑗  3 N , where ⃑ 𝑖 and ⃑ 𝑗 are two perpendicular unit vectors. After time 𝑑 seconds, where 𝑑 β‰₯ 0 , the body’s displacement relative to a fixed point is given by ⃑ 𝑠 =  ο€Ή π‘Ž 𝑑  ⃑ 𝑖 βˆ’ 𝑏 ο€Ή 𝑑 βˆ’ 𝑑  ⃑ 𝑗  2 2 m . 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 gβ‹…cm/s, at which point its kinetic energy was 5 670 g-wtβ‹…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 π‘š , and determine the time 𝑑 , in seconds, that the force acted for. Consider the acceleration due to gravity to be 9.8 m/s2.

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 1 . 9 Γ— 1 0 5 gβ‹…cm/s, determine the change in its kinetic energy. Consider the acceleration due to gravity to be 9.8 m/s2.

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 𝑔 = 9 . 8 / m s 2 .

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 𝑔 = 9 . 8 / m s 2 .

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 𝑔 = 9 . 8 / m s 2 .

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/s2 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.

Q25:

A ball fell vertically from the top of a tower. Just before it struck the ground, its momentum was 882 gβ‹…m/s, and its kinetic energy was 1 512 g-wtβ‹…m. Calculate the mass of the body π‘š and the height of the tower β„Ž . Consider the acceleration due to gravity to be 9.8 m/s2.

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