Barrons AP Calculus

(a)

(b)

(c)

(d)

(e)

Thus

s   increases   if  t > 3.

v   increases   if  t   <   0   or  t > 2.

Since   v   and a   have    the same    sign    if  0   <   t   <   2   or  if  t > 3,  the speed   increases

on  these   intervals.

The speed   when    t   =       equals  .

Figure  N4–16

The motion  is  shown   in  Figure  N4–16.  The particle    moves   to  the left    if  t   <   3

and to  the right   if  t > 3,  stopping    instantaneously when    t   =   0   and t   =   3,  but

reversing   direction   only    when    t   =   3.  Thus:

The particle travels a total of 54 units between t = 0 and t = 4.
(Compare with Example 13, where the function f (x) = x^4 − 4x^3 is investigated
for maximum and minimum values; also see the accompanying Figure N4–5.)

K. MOTION ALONG A CURVE: VELOCITY AND

ACCELERATION VECTORS