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 $
