The flow rate of water into a vat is given by r(t)= cases 6 & for 0 t 3, 2t & for t>3

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

The flow rate of water into a vat is given by

r(t)=\begin{cases} 6 & \text{for } 0\le t\le 3,\\ 2t & \text{for } t>3, \end{cases}

where

r(t)

is measured in liters per minute and

t

in minutes. The vat is initially empty at

t=0

. Determine the time

t>0

at which the accumulated volume of water in the vat first reaches

30

liters.