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

Complete step by step answer:
Power is defined as the rate of work done. It is equal to an amount of energy consumed per unit time. The unit of power is the ${\rm{J/s}}$ 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.
$P = F \cdot v$

Here, $P$ is power, $F$ is force, and $v$ is velocity.
As we know that $F = ma$. So,
$a = \dfrac{F}{m}$
Here, $a$ is acceleration, and $m$ is mass.

From equations of motion, we know that $v = u + at$. As we know that initial velocity will be zero. So,
$v = 0 + at \Rightarrow v = at$
Substituting $\dfrac{F}{m}$ for $a$ in the equation $v = at$, we get
$v = \left( {\dfrac{F}{m}} \right)t$
Substituting $\left( {\dfrac{F}{m}} \right)t$ for $v$ in the equation $P = F \cdot v$, 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 the time. So, the instantaneous power increases linearly with time.

Therefore, 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.