## sha0403 2 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. sauravshakya

can u find s'(t)

2. sha0403

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

3. sauravshakya

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

4. sha0403

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

5. sauravshakya

Because we are calculating avereage of two velocities

6. sha0403

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

7. sauravshakya

yes

8. sauravshakya

add three valocities and dvide it by

9. sauravshakya

3*

10. sha0403

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. sauravshakya

Just find s'(2)

12. sauravshakya

instantaneous means velocity of that body at that particular time

13. sauravshakya

got it?

14. wio

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. wio

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

16. wio

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. sauravshakya

2 has no units

18. sauravshakya

I was just calculating average velocity

19. wio

Wow, that's right. I was wrong.

20. sha0403

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

21. wio

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. sha0403

@sauravshakya and @wio ..thank u very much