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Worksheet: Power as the Rate of Work

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 𝑑 is given by the relation r i j ( 𝑑 ) = ο€Ή 7 𝑑  + ο€Ή 4 𝑑  3 2 . Given that 𝐹 is measured in newtons, π‘Ÿ in meters, and 𝑑 in seconds, write an expression for the power of force F at time 𝑑 .

  • A ο€Ή 3 3 3 2 𝑑 + 4 8 9 6 𝑑  3 W
  • B ο€Ή 7 4 9 7 𝑑 + 5 4 4 𝑑  3 W
  • C ο€Ή 1 6 6 6 𝑑 + 2 4 4 8 𝑑  3 W
  • D ο€Ή 1 4 9 9 4 𝑑 + 1 0 8 8 𝑑  3 W

Q8:

A body of mass 4 kg moves under the action of a force F . Its position vector at time 𝑑 is given by the relation r i j ( 𝑑 ) = ο€Ή 8 𝑑  + ο€Ή 5 𝑑  3 2 . Given that 𝐹 is measured in newtons, π‘Ÿ in meters, and 𝑑 in seconds, write an expression for the power of force F at time 𝑑 .

  • A ο€Ή 1 0 2 4 𝑑 + 1 8 0 0 𝑑  3 W
  • B ο€Ή 2 3 0 4 𝑑 + 2 0 0 𝑑  3 W
  • C ο€Ή 5 1 2 𝑑 + 9 0 0 𝑑  3 W
  • D ο€Ή 4 6 0 8 𝑑 + 4 0 0 𝑑  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 𝑑 seconds, is given by r i j ( 𝑑 ) = ο€Ή 2 𝑑 + 3 𝑑  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 𝑑 = 2 , and at 43 erg/s when 𝑑 = 4 , determine F .

  • A ( 9 + ) i j dynes
  • B ( βˆ’ 9 + ) i j dynes
  • C ( βˆ’ 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 𝑑 seconds, is given by r i j ( 𝑑 ) = ο€Ή 𝑑 βˆ’ 5 𝑑  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 𝑑 = 7 , and at 31 erg/s when 𝑑 = 2 , determine F .

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

Q13:

A constant force F , measured in dynes, is acting on a body. The displacement of the body, after 𝑑 seconds, is given by r i j ( 𝑑 ) = ο€Ή 2 𝑑 βˆ’ 6 𝑑  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 𝑑 = 6 , and at 14 erg/s when 𝑑 = 7 , determine F .

  • A ( 7 + 2 ) i j dynes
  • B ( βˆ’ 7 + 2 ) i j dynes
  • C ( 2 βˆ’ 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 .