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Worksheet: Using Integration to Find Power

In this worksheet, we will practice using integration to solve problems involving power as a function of time to find work, speed, or time.

Q1:

Find the time taken for a car of 1 236 kg to reach a speed of 126 km/h, given that the car started from rest and that the power of the engine is constant and equal to 103 horsepowers.

Q2:

Find the time taken for a car of 1 188 kg to reach a speed of 126 km/h, given that the car started from rest and that the power of the engine is constant and equal to 110 horsepowers.

Q3:

Find the time taken for a car of 972 kg to reach a speed of 126 km/h, given that the car started from rest and that the power of the engine is constant and equal to 90 horsepowers.

Q4:

The power of a machine is given by the relation 𝑃 = 3 𝑑 + 7 , where 𝑑 is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

Q5:

The power of a machine is given by the relation 𝑃 = 8 𝑑 βˆ’ 2 , where 𝑑 is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

Q6:

The power of a machine is given by the relation 𝑃 = 7 𝑑 + 3 , where 𝑑 is the time elapsed in seconds. Find the work done by the machine in the first 6 seconds.

Q7:

The power of an engine is given by hp, where is the time in seconds. Find the power of the engine when , the work done over the time interval , and the maximum power of the engine.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q8:

The power of an engine is given by hp, where is the time in seconds. Find the power of the engine when , the work done over the time interval , and the maximum power of the engine.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q9:

The power of an engine is given by hp, where is the time in seconds. Find the power of the engine when , the work done over the time interval , and the maximum power of the engine.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q10:

A car has mass 1 066 kg. At time 𝑑 seconds, its engine works at a rate of 𝑃 = ο€Ή 𝑑 + 9 𝑑  2 W . Given that at 𝑑 = 6 s the car’s speed is 78 km/h , find its speed at 𝑑 = 1 0 s . Give your answer to the nearest m/s.

Q11:

A car has mass 951 kg. At time 𝑑 seconds, its engine works at a rate of 𝑃 = ο€Ή 3 𝑑 + 9 𝑑  2 W . Given that at 𝑑 = 6 s the car’s speed is 73 km/h , find its speed at 𝑑 = 1 0 s . Give your answer to the nearest m/s.

Q12:

A car has mass 1 239 kg. At time 𝑑 seconds, its engine works at a rate of 𝑃 = ο€Ή 5 𝑑 + 9 𝑑  2 W . Given that at 𝑑 = 7 s the car’s speed is 57 km/h , find its speed at 𝑑 = 8 s . Give your answer to the nearest m/s.

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