Question

The motion of a body is given by the equation $\frac{dv}{dt}=6-3v$ where v is the speed in $m{s}^{-1}$ and t is time in s. The body is at rest at t = 0. The speed varies with time as

• A. $v=(1-e^{-3t})$
• B. $v=2(1-e^{-3t})$
• C. $v=(1+e^{-2t})$
• D. $v=2(1+e^{-2t})$

Answer 1

The correct option is B $v=2(1-e^{-3t})$

$\frac{dv}{dt}=6-3v$

$dv=(6-3v)dt$

$\int \frac{dv}{6-3v}=\int dt$

$\frac{-1}{3}ln(6-3v)=t+lnc$

$\frac{6-3v}{c}=e^{-3t}$

$6-3v=c{e}^{-3t}$

$v=\frac{1}{3}(6-c{e}^{-3t})$

at $t=0,v=0$

$c=6$

from above eqation

$v=2(1-e^{-3t})$

Option B