Page 51 - Math SL HB Sem 2

:
Example 30: A particle P moves in a straight line with velocity firnction v(1) 12 -3t + 2 m/s.
a) How far does P travel in the first 4 seconds ofmotion? [Ans: 5 % ]
b) Find the displacement ofP after 4 seconds.
[Ans: 5 % ]

SOLID OF REVOLUTION

A solid ofrevolution is formed by revdlving a plane region about a line - called the axis of
revolution-
We can obtain different shapes depending on the axis ofrevolution.
v v v

x x x Y

Rotation about the x-axis Ro about the

Using the same approach as that used when frnding the area ofa region enclosed by a
:
curve, the x-axis and the lines x : a and x b we have:
Then, the volume, v unitss, ofsuch a solid can be cut up into a large number ofslices or
discs, each having a width 6x and radius (x). The volume produced is the sum ofthe
volumes ofthese discs, i.e. Y
t' = .f(..)
i=a-l b-a
Y= lfl1iQ)l'&where&
i=0 n
So, as n --- co, 6x ---- 0 and so,

v= Ii* 1fl1:1x,11'6x

Typical disc:
ffi',;,;,,

I .'.6Y nll(.r)125x
=
withh =fu