# Lesson Worksheet: Power as the Rate of Work Mathematics

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

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 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 .

• Adynes
• Bdynes
• Cdynes
• Ddynes

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 .

Q8:

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.

Q9:

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, ,

Q10:

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

This lesson includes 17 additional questions and 185 additional question variations for subscribers.

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