If the force acting on a body is inversely pr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that the force $(F)$ is inversely proportional to the speed $(v)$,we have $F = \frac{k}{v}$,where $k$ is a constant.Using Newton's second la

Vedclass · Accepted Answer

linearly related to time

Vedclass · Answer

(C) Given that the force $(F)$ is inversely proportional to the speed $(v)$,we have $F = \frac{k}{v}$,where $k$ is a constant.Using Newton's second law,$F = ma = m \frac{dv}{dt}$.Substituting $F$,we get $m \frac{dv}{dt} = \frac{k}{v}$.Rearranging the terms,we get $mv \, dv = k \, dt$.Integrating both sides,we get $\int mv \, dv = \int k \, dt$,which gives $\frac{1}{2} mv^2 = kt + C$.Assuming the body starts from rest at $t = 0$,the constant $C = 0$.Thus,the kinetic energy $(KE = \frac{1}{2} mv^2)$ is equal to $kt$.Therefore,the kinetic energy is linearly related to time.

If the force acting on a body is inversely proportional to its speed,then its kinetic energy is

Similar Questions

The kinetic energy of a body of mass $3 \,kg$ and momentum $2 \,N-s$ is

If a man increases his speed by $2 \, m/s$,his kinetic energy is doubled. The original speed of the man is:

Two bodies with masses $M_1$ and $M_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momenta,then $p_1/p_2$ is equal to

$A$ bullet of mass $50 \ g$ is fired with a speed $100 \ m/s$ on a plywood and emerges with $40 \ m/s$. The percentage loss of kinetic energy is:

An object of $1 \, kg$ mass has a momentum of $10 \, kg \cdot m/s$. Then,the kinetic energy of the object will be .............. $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module