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Worksheet: Power as the Rate of Work

In this worksheet, we will practice calculating the power of a moving body given that its motion and the force acting on it are represented in vector notation.

Q1:

A particle is moving under the action of the force . Its position vector at time is given by the relation . Find the rate of the work done by the force at .

Q2:

A particle is moving under the action of the force . Its position vector at time is given by the relation . Find the rate of the work done by the force at .

Q3:

A particle of mass 4 g is moving under the action of two forces and , where dynes and dynes. The position vector of the particle is given as a function of time by , where and are constants. Determine, in ergs per second, the power at which the resultant force acts on the particle 8 seconds after the start of motion.

Q4:

A particle of mass 2 g is moving under the action of two forces and , where dynes and dynes. The position vector of the particle is given as a function of time by , where and are constants. Determine, in ergs per second, the power at which the resultant force acts on the particle 6 seconds after the start of motion.

Q5:

A body of mass 3 kg moves under the action of a force N. At time seconds, the velocity of the body is given by . Find, in terms of , the power of the force, .

  • A W
  • B W
  • C W
  • D W
  • E W

Q6:

A body of mass 2 kg moves under the action of a force N. At time seconds, the velocity of the body is given by . Find, in terms of , the power of the force, .

  • A W
  • B W
  • C W
  • D W
  • E W

Q7:

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 r i j ( 𝑡 ) = 7 𝑡 + 4 𝑡 3 2 . 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 .

  • A 3 3 3 2 𝑡 + 4 8 9 6 𝑡 3 W
  • B 7 4 9 7 𝑡 + 5 4 4 𝑡 3 W
  • C 1 6 6 6 𝑡 + 2 4 4 8 𝑡 3 W
  • D 1 4 9 9 4 𝑡 + 1 0 8 8 𝑡 3 W

Q8:

A body of mass 4 kg moves under the action of a force F . Its position vector at time 𝑡 is given by the relation r i j ( 𝑡 ) = 8 𝑡 + 5 𝑡 3 2 . 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 .

  • A 1 0 2 4 𝑡 + 1 8 0 0 𝑡 3 W
  • B 2 3 0 4 𝑡 + 2 0 0 𝑡 3 W
  • C 5 1 2 𝑡 + 9 0 0 𝑡 3 W
  • D 4 6 0 8 𝑡 + 4 0 0 𝑡 3 W

Q9:

A particle of unit mass is moving under the action of a force . Its displacement, as a function of time, is given by . Find the value of when .

Q10:

A particle of unit mass is moving under the action of a force . Its displacement, as a function of time, is given by . Find the value of when .

Q11:

A constant force F , measured in dynes, is acting on a body. The displacement of the body, after 𝑡 seconds, is given by r i j ( 𝑡 ) = 2 𝑡 + 3 𝑡 2 c m , where i and j are two perpendicular unit vectors. Given that the force F was working at a rate of 35 erg/s when 𝑡 = 2 , and at 43 erg/s when 𝑡 = 4 , determine F .

  • A ( 9 + ) i j dynes
  • B ( − 9 + ) i j dynes
  • C ( − 9 ) i j dynes
  • D ( + 9 ) i j dynes

Q12:

A constant force F , measured in dynes, is acting on a body. The displacement of the body, after 𝑡 seconds, is given by r i j ( 𝑡 ) = 𝑡 − 5 𝑡 2 c m , where i and j are two perpendicular unit vectors. Given that the force F was working at a rate of 71 erg/s when 𝑡 = 7 , and at 31 erg/s when 𝑡 = 2 , determine F .

  • A ( − 3 + 4 ) i j dynes
  • B ( 3 + 4 ) i j dynes
  • C ( 4 + 3 ) i j dynes
  • D ( 4 − 3 ) i j dynes

Q13:

A constant force F , measured in dynes, is acting on a body. The displacement of the body, after 𝑡 seconds, is given by r i j ( 𝑡 ) = 2 𝑡 − 6 𝑡 2 c m , where i and j are two perpendicular unit vectors. Given that the force F was working at a rate of 6 erg/s when 𝑡 = 6 , and at 14 erg/s when 𝑡 = 7 , determine F .

  • A ( 7 + 2 ) i j dynes
  • B ( − 7 + 2 ) i j dynes
  • C ( 2 − 7 ) i j dynes
  • D ( 2 + 7 ) i j dynes

Q14:

A body of mass 5 kg is moving under the action of the force measured in newtons. Its position vector after seconds is given by Find the work done by the force over the interval .

Q15:

A body of mass 3 kg is moving under the action of the force measured in newtons. Its position vector after seconds is given by Find the work done by the force over the interval .

Q16:

A body of mass 8 kg is moving under the action of the force measured in newtons. Its position vector after seconds is given by Find the work done by the force over the interval .

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