## math456 3 years ago If a ball is thrown into the air with a v of 40 ft/s, it's height in ft t seconds late is given by y= 40t-16t^2. Find the avg velocity for the time period beginning when t=2 & lasting 0.5 sec, 0.05 sec?

1. Algebraic!

so the distance covered / the time interval is what you're looking for...

2. Algebraic!

do you know how to find the distance covered between t=2 and t=2.5?

3. math456

The average velocity!

4. math456

Yea it's like u plug in the 2 in the equation and then distance covered in 2-distance coverd in 2.5/2-2.5

5. Algebraic!

yes

6. math456

So in this case is .5 sec= 0?

7. Algebraic!

no.

8. math456

And 0.05=7.2

9. Algebraic!

find y(2) find y(2.5)

10. Algebraic!

then find the difference between those two heights

11. Algebraic!

then divide by the time interval (.5s)

12. math456

But 2.5 is not in the question..

13. Algebraic!

k

14. Algebraic!

2 + .5 = ?

15. math456

2.5 ohh gotch ya so all I do is divide by the 0.5, 0.05?

16. math456

So for 0.5 it's 32?

17. Algebraic!

let me check

18. math456

Okay

19. Algebraic!

yep

20. math456

And for 0.05 is 320?

21. Algebraic!

don't think so... how'd you get that

22. math456

Y(2)-y(2.5)/0.05

23. Algebraic!

naw...

24. Algebraic!

y(2) and y(2.05)

25. math456

U r adding the values to 2.0?

26. Algebraic!

height at 2 seconds and height .05 seconds later ( y(2.05) )

27. math456

so for 0.01 second its y(2)-y(2.01)

28. Algebraic!

\[(d _{f} - d _{i})/(t _{f} -t _{i})\]

29. Algebraic!

yep

30. math456

okay how abt if i want to find the estimate instantaneous velocity when t=2

31. math456

sorry t=1*

32. Algebraic!

if you're allowed to use calculus you just take the derivative...

33. Algebraic!

if not, you take the limit of the avg. velocity expression as t->0

34. math456

ummm not sure what u meant so when t=2 its t>0

35. Algebraic!

the third alternative is using the equation that you might've been given where the derivative is already taken for you...

36. Algebraic!

something like \[V(t) = V _{o} +at\]

37. Algebraic!

seen that before?

38. math456

can i just do like 32-14.76M0.5-0.05N

39. math456

yea i hv seen it

40. math456

sorry here m is the divide sign

41. Algebraic!

The three ways I mentioned are the ways to do it, not sure what you typed there or what you're trying to do.

42. Algebraic!

You all good on this? Or do you have another question?

43. math456

how how can i take the limit of avg. velocity at t>0?

44. math456

@Algebraic!

45. Algebraic!

like:

46. Algebraic!

for a specific value of t?

47. math456

t=2

48. Algebraic!

I'll use the sketch pad to show you

49. math456

okay, thanks

50. Algebraic!

|dw:1347077529182:dw|

51. Algebraic!

that's the first term...

52. math456

hmmm how do I find the delta t value?

53. Algebraic!

|dw:1347077587650:dw|

54. Algebraic!

that's the second term

55. math456

okay.

56. Algebraic!

all that gets divided by delta t

57. Algebraic!

then you take the limit as delta t ->0

58. math456

so the limit as x approaches to 0 is -16

59. math456

for inst. velocity?

60. Algebraic!

should be -24

61. math456

let me check again..

62. math456

okay got it nw..

63. Algebraic!

cool;)

64. math456

thanks for ur help..

65. Algebraic!

No problem!