Question

The initial velocity of an object is 40 m/s. The acceleration a of the object is given by the following expression. a=-0.1 v, where v is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be

Answer 1

Given: $U=40\frac{m}{s},a=-0.1v,V=?,t=3s$
$a=\frac{dv}{dt}=-0.1v$
${\int }_{40}^v\frac{dv}{v}={\int }_0^3-0.1dt$
$\left[ln\right(v){]}_{40}^v=-0.1[t]$
$ln\left(v\right)-ln40=-0.1\left[3.0\right]=-0.3$
$ln\left(v\right)=ln40-0.3$
$ln\left(v\right)=3.38887$
or $v=e^{3.38887}=29.63\frac{m}{s}$