Work Energy And Power Question 143

Question: The kinetic energy of a particle moving along a straight line increases uniformly with respect to the distance travelled by it. The force acting on the particle is ( $ v $ is the speed of particle at any time)

Options:

A) constant

B) proportional to $ v $

C) proportional to $ v^{2} $

D) inversely proportional to $ v $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ KE\propto x\Rightarrow KE=C _{x}\Rightarrow \frac{1}{2}mv^{2} $

$ ~=Cx\frac{1}{2}m2v\frac{dv}{dt}=C\frac{dx}{dt}\Rightarrow mv\frac{dv}{dt}=Cv $

$ m\frac{dv}{dt}=C\Rightarrow ma=C $

$ \Rightarrow F=C\to constant $



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