Question

If force F acting on a body is given as \[F \propto \dfrac{1}{v},\] then its kinetic energy will be proportional to time as:
A. t
B. \[\dfrac{1}{{{t^2}}}\]
C. \[\dfrac{1}{t}\]
D. \[\sqrt t \]

Answer 1

Hint: Use the formula, W = Fs = KE. Kinetic energy, a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy. Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m$v^2$. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.
W = work, F = force, s = distance, KE = kinetic energy.
Here, work done is converted to kinetic energy.

Complete step by step answer:
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
Work done on a body is equal to the increase in the energy i.e., kinetic energy of the body, for work transfers energy to the body.
Given, \[F\propto \dfrac{1}{v}\]
Work done is converted to kinetic energy W = Fs = KE
W = work done, F = force, s = Distance, KE = Kinetic energy
W = Fs = KE
\[ \Rightarrow \,KE \propto \dfrac{1}{v} \times s\]
\[ \Rightarrow \,KE \propto \dfrac{s}{v} = \dfrac{s}{{s/t}} = t\,\,\left[ {\text{Since}\,v = \dfrac{s}{t}} \right]\]
\[ \Rightarrow \,KE \propto t\]

So, the correct answer is “Option A”.

Note: Relation between work done and energy stored is required to solve this question. Kinetic energy is the energy an object has because of its motion. If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work. Kinetic energy can be transferred between objects and transformed into other kinds of energy.