A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is:

Question

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is: (A) √(m k/2) t- (1/2) (B) √m k t- (1/2) (C) √2 m k t- (1/2) (D) (1/2)√m k t- (1/2)

Tardigrade Admin · Accepted Answer

Fv=constant=k (m d v/d t)v=k displaystyle ∫ v d v= displaystyle ∫ (k/m)dt (v2/2)=(k/m)t v=√(2 k/m) t F=(m d v/d t) =m √(2 k/m)(1/2)t- (1/2) =√(m k/2) t- (1/2)

Q. A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest the force on the particle at time $t$ is:

$\frac{mk}{2} t^{- \frac{1}{2}}$

$mk t^{- \frac{1}{2}}$

$2 mk t^{- \frac{1}{2}}$

$\frac{1}{2} mk t^{- \frac{1}{2}}$

$F v = co n s t an t = k$
$\frac{m d v}{d t} v = k$
$\int v d v = \int \frac{k}{m} d t$
$\frac{v ^{2}}{2} = \frac{k}{m} t$
$v = \frac{2 k}{m} t$
$F = \frac{m d v}{d t}$
$= m \frac{2 k}{m} \frac{1}{2} t^{- \frac{1}{2}}$
$= \frac{mk}{2} t^{- \frac{1}{2}}$

Q. A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is:

2mk​​t−21​

mk​t−21​

2mk​t−21​

21​mk​t−21​