Question

Define power & show that power is equal to the product of force and velocity.

Answer 1

Hint: Power is a unit to measure the work we have done. It can be explained in many ways. Because the work is done in a different unit. It can be explained in terms of voltage, energy, torque, etc. The rate of doing work is called Power.

Complete step by step answer:
(i) Power is the measure of the amount of work we did in a given limit. In other words, power can be defined as the amount of work we did in converting the energy from one form into another in a given time.
(ii) From this explanation, we can say that power,
\[P = \dfrac{{dW}}{{dt}}\]
As we know that, Work done, W is the product of Force (F) and displacement(r)
\[P = \dfrac{{F.dr}}{{dt}}\]
We say the ratio of displacement to the time taken as velocity. Hence the above equation of power changes in to,
\[P = \vec F.\vec v\]
The arrow mark denotes both force and velocity are vector quantities. And we showed that power is the product of force and velocity. Hence we showed that power is the product of force and velocity.

Therefore, the particle traveled a distance of 6.5m in a straight line in 5 seconds. Hence the correct option is C.

Additional information:
(i) Even though both force and velocity are vector quantities, power is a scalar quantity. It does not depend on direction. It has the only magnitude because it is an ‘amount’ of doing work which only has magnitude.
(ii) The SI unit of power is the watt (W). One watt is defined as the 1 joule of work done in one second.
(iii) Power can be derived in the unit \[kg{m^2}{s^{ - 3}}\]. And the dimension of power is \[{L^2}M{T^{ - 3}}\]. Power can be derived in several units. Among the units, the traditional way of describing power is ‘horsepower’. One horsepower is equal to 745.7watts.
(iv) One Horse Power (hp) is the amount of work done when the horse lifts 550 pounds by 1 foot in 1 second.
(v) The term power can be defined for many works. For example, in current electricity, we say power is the product of voltage and current. And in kinetics, we say power is the product of force and velocity. Like this, power can be described in many terms.
Some of the ways of defining power are,
(a) \[P = V \times I\]
(b) \[P = T \times \omega \]
(c) \[P = \dfrac{E}{t}\]

Note:
As a whole, power is defined as the amount of work done in a certain time. Here we use the force and velocity. If it is in current electricity, we describe power as the product of voltage and current. According to the way of work, the definition of power will change. If the power is measured for the rotational motion, we say that power is the product of torque and angular velocity.