Question

a ball thrown straight up into the air so that its height in feet after t seconds is given by s(t)= 128t-16t^2.. so, find the average velocity of the ball during tie interval (2,2.1)

Answer 1

can u find s'(t)

Answer 2

yes.. after that i get 128-32t.. so what should i do that given time interval (2, 2.1)

Answer 3

U need to find {s'(2) + s'(2.1)}/2

Answer 4

why it divide by 2? can u explain to me?

Answer 5

Because we are calculating avereage of two velocities

Answer 6

oh like that..if we want to calculate average between 3 velocity,, we should divide by 3 also?

Answer 7

yes

Answer 8

add three valocities and dvide it by

Answer 9

3*

Answer 10

ok.... i would like to ask u something.. if the question ask to find instantaneous velocity at t=2.. what the mean of instantaneous/

Answer 11

Just find s'(2)

Answer 12

instantaneous means velocity of that body at that particular time

Answer 13

got it?

Answer 14

Umm, one thing I'd like to note is that @sauravshakya 's method for finding the average value works for lines. In this case velocity is indeed linear so it will work, though.

Answer 15

Wait, actually @sauravshakya , the units don't seem to work out with your method.

You have \(\frac{m/s}{s}\), which is acceleration.

Answer 16

I think we don't need to do any calculus at all here. It's just: \[ \large
\frac{s(t_f)-s(t_i)}{t_f-t_i}
\]

Answer 17

2 has no units

Answer 18

I was just calculating average velocity

Answer 19

Wow, that's right. I was wrong.

Answer 20

@wio your formula when i should use it? what the kind of question?

Answer 21

Anyway, I'm thinking that the average velocity, given velocity is: \[ \large
\overline{v(t)} = \frac{1}{t_f-t_i}\int_{t_i}^{t_f} v(t) dt
\]Note that \(s(t) = \int v(t) dt \), which gives us (by fundamental theorem of calc: \[
\frac{s(t_f) - s(t_i)}{t_f - t_i}
\]

Answer 22

@sauravshakya and @wio ..thank u very much