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Lesson Worksheet: Power as the Rate of Work Mathematics

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In this worksheet, we will practice defining the power of a force as the derivative of the work done by the force.

Q1:

Complete the following: The rate at which work is done is called .

  • Awork
  • Bpotential energy
  • Cpower
  • Dkinetic energy

Q2:

Complete the following: If the work done by a given force at time 𝑡 seconds is given by 𝑊(𝑡)=2𝑡+3𝑡+9J, the power of this force at 𝑡=5s equals .

Q3:

The work done by an engine at time 𝑡 is given by the relation 𝑊(𝑡)=−12(2𝑡)cosJ. Find the power of the engine as a function of time.

  • A24(2𝑡)sin W
  • B−24(2𝑡)sin W
  • C6(2𝑡)sin W
  • D−6(2𝑡)sin W
  • E24(2𝑡)cos W

Q4:

The work done by an engine at time 𝑡 is given by the relation 𝑊(𝑡)=14𝑒J. Find the power of the engine as a function of time.

  • A28𝑒 W
  • B−28𝑒 W
  • C16𝑒 W
  • D7𝑒 W
  • E14𝑒 W

Q5:

The work done by an engine at time 𝑡 is given by the relation 𝑊(𝑡)=15+𝑡J. Find the power of the engine as a function of time.

  • A−15+𝑡 W
  • B5(5+𝑡) W
  • C−5(5+𝑡) W
  • D−1(5+𝑡) W
  • E1(5+𝑡) W

Q6:

A body of mass 17 kg moves under the action of a force F. Its position vector at time 𝑡 is given by the relation rij(𝑡)=7𝑡+4𝑡. Given that 𝐹 is measured in newtons, 𝑟 in meters, and 𝑡 in seconds, write an expression for the power of force F at time 𝑡.

  • A3,332𝑡+4,896𝑡 W
  • B7,497𝑡+544𝑡 W
  • C14,994𝑡+1,088𝑡 W
  • D1,666𝑡+2,448𝑡 W

Q7:

A particle is moving under the action of the force Fij=8+5. Its position vector at time 𝑡 is given by the relation rij(𝑡)=3𝑡−𝑡−4+52𝑡+10𝑡+5. Find the rate of the work done by the force at 𝑡=3.

Q8:

The power of an engine at time 𝑡 seconds is given by 𝑃(𝑡)=12𝑡+8𝑡W. Find the work done by the engine between 𝑡=2s and 𝑡=3s.

Q9:

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

Q10:

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 metric horsepower.

This lesson includes 52 additional questions and 194 additional question variations for subscribers.

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