Water is pumped into a storage tank at a variable rate given

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Water is pumped into a storage tank at a variable rate given, in litres per minute, by

R(t)=a t^{2}+6

, where

t

is the time in minutes

(t\ge 0)

and

a

is a constant. The volume of water in the tank at time

t

minutes is

V(t)=\displaystyle\int R(t)\,dt

. It is known that the tank is empty at

t=0

and that it contains

160

litres after

4

minutes. (i) Obtain the expression for

V(t)

, including the constant of integration

C

. (ii) Using the condition

V(0)=0

, determine the value of

C

. (iii) Using the additional information

V(4)=160

, calculate the value of

a