Question

A force \[(7\hat{i}+6\hat{k})\]newton makes a body move on rough plane with a velocity of $(3\hat{j}+4\hat{k})m{{s}^{-1}}$. The power of watt is
$\begin{align}
  & a)24 \\
 & b)34 \\
 & c)21 \\
 & d)45 \\
\end{align}$

Answer 1

Hint: Power is simply the force times the velocity. As both the power and velocity are given in vector form, the power can be calculated as the dot product of the force acting on the body and the velocity of the body.
Formulas used:
$P=F.v$

Complete answer:
Power is calculated as the work done per unit time. It is also known as rate of doing work or rate of using energy. Now, as work done is equal to force times the displacement, displacement divided by time can be written as velocity which results as ,
Power is equal to force times the velocity.
$\begin{align}
  & P=F.v \\
 & P=(7\hat{i}+6\hat{k}).(3\hat{j}+4\hat{k}) \\
 & P=24watts \\
\end{align}$
Therefore, the correct option is option a.

Additional information:
Power is the amount of energy transferred or converted per unit time. In the unit system, the unit of power is watt, equal to one joule per second. We call power as activity in usual terms. It is a scalar quantity. Power doesn’t represent any direction. In rotational mechanics, power is the product of torque produced by the rotating object and the angular velocity. In jet propelled vehicles, power is equal to the product of thrust in the engine and the velocity of the vehicle. In mechanics, power is the combination of forces and movement. Mechanical power is also described as the time derivative of work. Integrals are used in this case. If any mechanical system is present such that the input power is equal to output power, it is impossible. No machine has ever gained hundred percent efficiency.

Note:
Power can usually also be in negative value. It simply means that power is flowing in the opposite direction. Power is a scalar quantity. It only represents its magnitude by it doesn’t tell us about the direction in which the power is flowing.