## sha0403 Group Title 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) one year ago one year ago

1. sauravshakya Group Title

can u find s'(t)

2. sha0403 Group Title

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

3. sauravshakya Group Title

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

4. sha0403 Group Title

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

5. sauravshakya Group Title

Because we are calculating avereage of two velocities

6. sha0403 Group Title

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

7. sauravshakya Group Title

yes

8. sauravshakya Group Title

add three valocities and dvide it by

9. sauravshakya Group Title

3*

10. sha0403 Group Title

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 Group Title

Just find s'(2)

12. sauravshakya Group Title

instantaneous means velocity of that body at that particular time

13. sauravshakya Group Title

got it?

14. wio Group Title

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 Group Title

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 Group Title

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 Group Title

2 has no units

18. sauravshakya Group Title

I was just calculating average velocity

19. wio Group Title

Wow, that's right. I was wrong.

20. sha0403 Group Title

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

21. wio Group Title

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 Group Title

@sauravshakya and @wio ..thank u very much