## anonymous 3 years ago 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)

1. anonymous

can u find s'(t)

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

Because we are calculating avereage of two velocities

6. anonymous

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

7. anonymous

yes

8. anonymous

add three valocities and dvide it by

9. anonymous

3*

10. anonymous

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

11. anonymous

Just find s'(2)

12. anonymous

instantaneous means velocity of that body at that particular time

13. anonymous

got it?

14. anonymous

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.

15. anonymous

Wait, actually @sauravshakya , the units don't seem to work out with your method. You have $$\frac{m/s}{s}$$, which is acceleration.

16. anonymous

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

17. anonymous

2 has no units

18. anonymous

I was just calculating average velocity

19. anonymous

Wow, that's right. I was wrong.

20. anonymous

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

21. anonymous

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: $\frac{s(t_f) - s(t_i)}{t_f - t_i}$

22. anonymous

@sauravshakya and @wio ..thank u very much