# Worksheet: Power as the Rate of Work

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

**Q2: **

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 .

- A60 power units
- B228 power units
- C476 power units
- D124 power units

**Q3: **

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

**Q4: **

A body of mass 17 kg moves under the action of a force . Its position vector at time is given by the relation . Given that is measured in newtons, in meters, and in seconds, write an expression for the power of force at time .

- A W
- B W
- C W
- D W

**Q5: **

A particle of mass 4 g is moving under the action of two forces and , where and . 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.

**Q6: **

A constant force , measured in dynes, is acting on a body. The displacement of the body, after seconds, is given by , where and are two perpendicular unit vectors. Given that the force was working at a rate of 35 erg/s when , and at 43 erg/s when , determine .

- A dynes
- B dynes
- C dynes
- D dynes

**Q7: **

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 .

**Q9: **

A particle of mass 2 g is moving under the action of two forces and , where and . 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.

**Q10: **

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

**Q11: **

A body of mass 4 kg moves under the action of a force . Its position vector at time is given by the relation . Given that is measured in newtons, in meters, and in seconds, write an expression for the power of force at time .

- A W
- B W
- C W
- D W

**Q12: **

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 .

- A38 power units
- B188 power units
- C373 power units
- D4 power units

**Q13: **

A constant force , measured in dynes, is acting on a body. The displacement of the body, after seconds, is given by , where and are two perpendicular unit vectors. Given that the force was working at a rate of 71 erg/s when , and at 31 erg/s when , determine .

- A dynes
- B dynes
- C dynes
- D dynes

**Q14: **

A constant force , measured in dynes, is acting on a body. The displacement of the body, after seconds, is given by , where and are two perpendicular unit vectors. Given that the force was working at a rate of 6 erg/s when , and at 14 erg/s when , determine .

- A dynes
- B dynes
- C dynes
- D dynes

**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 .

**Q17: **

The power of a machine is given by the relation , where is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

**Q18: **

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 , ,

**Q19: **

The power of an engine at time seconds is given by . Find the work done by the engine between and .

**Q20: **

A car has mass 1,066 kg. At time seconds, its engine works at a rate of . Given that at the carβs speed is 78 km/h , find its speed at . Give your answer to the nearest m/s.