-Dista

nce.Time

f,unctions

-In

these

sases,

the derivative

messures

the

instantaneous

rate

of change of

distance

with

time.

This is itrstantanesus

Vclocity oriust

Velocrty at

an

instant.

tsxample:

You

throw a ball

directly

upward

with

a

velocity

of

40 fi/sec.

It's heiglrt,

in feet,

afts

t seconds,

is

givenbe

S

=

4ft

-

t' .

(a)

Find

the everage

veiocrty

between

11

&1,=2.3

secs.

(b)

Find the instantaneous

velocity

atF? secs.

(

o)

How

high does

it

go?

(d)

How

long

does

it take

to csme back

to

your

hand?

Note, since

S=(t),

you

can use

qq=+Ot-t'

.

-Time

perrritting

do:

flad

f

'(x)

for

(x)

=

3-2x-4x2 usingthe

definition

of f

'

(x).