Question

What is power? Show that power= force* velocity? Calculate the power of a body of mass $10Kg$ accelerating with $10{\text{ m/s}}$ acquires a velocity of $5{\text{ m/s}}$.

Answer 1

Hint This is quite an easy question. We can directly get the answer by substituting the given values. To show that power= force* velocity, we know the formula for power, substitute the work done formula in power formula and use that same derivation to find the power of the given body.

Complete step by step answer
Power is the rate of doing work. It is the energy or strength of a body. Power is given by the ratio of work done by time. The unit of power is Watt (W).
$ \Rightarrow P = \dfrac{W}{t}{\text{ }} \to {\text{1}}$
P is the power
W is the work done
Work done is the product of force and displacement.
$ \Rightarrow W = F \times d$
F is force
d is distance travelled or displacement
Then power can be written as
$ \Rightarrow P = \dfrac{{F \times d}}{t}$
$ \Rightarrow P = F \times \dfrac{d}{t}{\text{ }} \to {\text{2}}$
We know that displacement by time taken is velocity.
$ \Rightarrow v = \dfrac{d}{t}$
Substituting the above in equation 2
$ \Rightarrow P = F \times v$
V is the velocity.
Hence it is proved that power is the product of force and velocity
Given that,
Mass of the body, $m = 10Kg$
Acceleration of the body, $10{\text{ m/s}}$
Velocity of the body, $5{\text{ m/s}}$
The power of the body=?
Power of the body is given by the formula
$ \Rightarrow P = F \times v$
We know that force is the product of mass and acceleration.
$ \Rightarrow P = m \times a \times v$
m is the mass
a is the acceleration
Substituting the given value
$ \Rightarrow P = m \times a \times v$
$ \Rightarrow P = 10 \times 10 \times 5$
$ \Rightarrow P = 500W$

Note The term power also exists in electricity, electric power is the rate of doing work when voltage is applied. When voltage is applied the work done is the product of voltage current and time. Then,
$ \Rightarrow P = \dfrac{W}{t}$
$ \Rightarrow P = \dfrac{{VIt}}{t}$
$ \Rightarrow P = VI$
P is the power
I is the current
t is the time