Question

Instantaneous power of constant force acting on a particle moving in a straight line under the action of this force
(A) Is constant
(B) Increases linearly with time
(C) Decreases linearly with time
(D) Either increases or decreases linearly with time

Answer 1

To answer this problem we must know the relation of force with velocity, and the relation of time with velocity. In the solution, we will use the equation of motions given by Newton also commonly called Newton’s equation of motion. They show the relation between several motions defining physical quantities like time, displacement, speed, and acceleration of the body in motion.

Formula used:
In this question, we will use this formula
$\Rightarrow F = \dfrac{{{\mu _0}{M_1}{M_2}}}{{4\pi {d^2}}}$
where, $F$ is the force between two magnetic poles of strength ${M_1}$ and ${M_2}$ at a distance of $d$ .

Complete step by step solution:
Power is known as the rate of work done. It is equal to the amount of energy consumed per unit of time. The unit of power is the $J/s$ in SI system. It is also expressed in Watt.
The instantaneous power is given by the dot product of force and velocity which can be written as follows.
$P = F.v$
Here, $P$ is the power, $F$ is the force, and $v$ is velocity.
As we know that $F = ma$ . So,
$v = 0 + at \Rightarrow v = at$
On substituting $\dfrac{F}{m}$ for $a$ in the equation $v = at$ , we get
$v = \left( {\dfrac{F}{m}} \right)t$
On substituting $\left( {\dfrac{F}{m}} \right)t$ for $v$ in the equation $P = F.v$ , we get
$P = \left( {\dfrac{{{F^2}}}{m}} \right)t$
$\Rightarrow P \propto t$
From the above relation, we can see that power is directly proportional to time. So, the instantaneous power increases linearly with time.
Hence, from the other options, only option (B) is the correct answer.

Note:
Make sure to use the correct relation between each parameter and also remember that the object is initially at rest so the initial speed of the object will be zero. We must know about the instantaneous power and its formula.