# 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.

**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

**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 βseconds, 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 .

- Adynes
- Bdynes
- Cdynes
- Ddynes

**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

**Q13: **

A constant force , measured in dynes, is acting on a body. The displacement of the body, after βseconds, 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 .

- Adynes
- Bdynes
- Cdynes
- Ddynes

**Q14: **

A constant force , measured in dynes, is acting on a body. The displacement of the body, after βseconds, 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 .

- Adynes
- Bdynes
- Cdynes
- Ddynes

**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.