Question

f a ball is thrown straight up into the air with an initial velocity of 40 ft/s, its height in feet after t second is given by y = 40 t - 16 t^2. Find the average velocity for the time period beginning when t = 1 and lasting
(i) 0.5 seconds

(ii) 0.1 seconds

(iii) 0.01 seconds

Finally based on the above results, guess what the instantaneous velocity of the ball is when t =1.

Answer 1

to find avg velocity, use slope formula
\[\frac{f(b) - f(a)}{b-a}\]
where a,b are "t" values

Answer 2

what values do u put in for a,b

Answer 3

"b" is ending time .... t = 1.5 or 1.1 or 1.01
"a" is starting time .... t=1

Answer 4

43.68-24/1.5-1= 39.36 is ths correct??

Answer 5

almost how do you get 43.68?
did you plug in 1.5 for t?

Answer 6

yes

Answer 7

http://www.wolframalpha.com/input/?i=40t+-16t%5E2%2C+t%3D1.5
should get 24

Answer 8

sorry my mistake hit plus instead of -

Answer 9

so 24-24 = 0
avg velocity for first part is 0

Answer 10

yes i got that there now

Answer 11

and what way do i work out the rest ??

Answer 12

do same thing, instead of 1.5 use 1.1 and 1.01

Answer 13

avg velocity should increase each time and approach 8 which is the instantaneous velocity at t=1

Answer 14

thanks very much very helpful