Question

If a ball is thrown into the air with a v of 40 ft/s, it's height in ft t seconds late is given by y= 40t-16t^2. Find the avg velocity for the time period beginning when t=2 & lasting 0.5 sec, 0.05 sec?

Answer 1

so the distance covered / the time interval is what you're looking for...

Answer 2

do you know how to find the distance covered between t=2 and t=2.5?

Answer 3

The average velocity!

Answer 4

Yea it's like u plug in the 2 in the equation and then distance covered in 2-distance coverd in 2.5/2-2.5

Answer 5

yes

Answer 6

So in this case is .5 sec= 0?

Answer 7

no.

Answer 8

And 0.05=7.2

Answer 9

find y(2) find y(2.5)

Answer 10

then find the difference between those two heights

Answer 11

then divide by the time interval (.5s)

Answer 12

But 2.5 is not in the question..

Answer 13

k

Answer 14

2 + .5 = ?

Answer 15

2.5 ohh gotch ya so all I do is divide by the 0.5, 0.05?

Answer 16

So for 0.5 it's 32?

Answer 17

let me check

Answer 18

Okay

Answer 19

yep

Answer 20

And for 0.05 is 320?

Answer 21

don't think so... how'd you get that

Answer 22

Y(2)-y(2.5)/0.05

Answer 23

naw...

Answer 24

y(2) and y(2.05)

Answer 25

U r adding the values to 2.0?

Answer 26

height at 2 seconds and height .05 seconds later ( y(2.05) )

Answer 27

so for 0.01 second its y(2)-y(2.01)

Answer 28

\[(d _{f} - d _{i})/(t _{f} -t _{i})\]

Answer 29

yep

Answer 30

okay how abt if i want to find the estimate instantaneous velocity when t=2

Answer 31

sorry t=1*

Answer 32

if you're allowed to use calculus you just take the derivative...

Answer 33

if not, you take the limit of the avg. velocity expression as t->0

Answer 34

ummm not sure what u meant so when t=2 its t>0

Answer 35

the third alternative is using the equation that you might've been given where the derivative is already taken for you...

Answer 36

something like
\[V(t) = V _{o} +at\]

Answer 37

seen that before?

Answer 38

can i just do like 32-14.76M0.5-0.05N

Answer 39

yea i hv seen it

Answer 40

sorry here m is the divide sign

Answer 41

The three ways I mentioned are the ways to do it, not sure what you typed there or what you're trying to do.

Answer 42

You all good on this? Or do you have another question?

Answer 43

how how can i take the limit of avg. velocity at t>0?

Answer 44

@Algebraic!

Answer 45

like:

Answer 46

for a specific value of t?

Answer 47

t=2

Answer 48

I'll use the sketch pad to show you

Answer 49

okay, thanks