# 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 . 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

Q8:

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

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 , 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

Q12:

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

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 6 erg/s when , and at 14 erg/s when , determine .

• A dynes
• B dynes
• C dynes
• D 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 .