If a ball is thrown in the air with a velocity 44 ft/s,?

Question

its height in feet t seconds later is given by y = 44t - 16t2.

Find the average velocity for the time period beginning when t = 2 and lasting 0.5 second.

Find the average velocity for the time period beginning when t = 2 and lasting 0.1 second.


Estimate the instantaneous velocity when t = 2.

Answer 1

y = 44t - 16t^2

a)
average velocity begining at 2 and lasting for 0.5 sec
(average velocity between 2 and 2.5)=

y(2) - y(2.5)/0.5 =

44(2) - 16(2)^2 - [44(2.5) - 16(2.5)^2]/0.5 =

(88 - 64)-[110 - 100]/0.5 =
24-10/0.5 =
14/0.5 = 28 ft/s

b)

average vel between t =2 and lasting for 0.1 sec

y(2) - y(2.1)/0.1 =

44(2) - 16(2)^2 - [44(2.1) - 16(2.1)^2]/0.1 =

(88 - 64) -[92.4 - 70.56]/0.1 =

24 - 21.84/0.1 =

21.6 ft/s

c) instantaneous v at t = 2 = y'(2)

y' = 44 - 32t

y'(2) = 44 - 32(2) =

44 - 64 =

-20 ft/s

Answer 2

Hi,
We want to use the equation:
v = d/t. (Where d = distance travelled.)
So, we need the distance travelled from t =2 to t=2.5. We just plug those numbers into the equation and subtract the two distances. Let's call the distance for t=2, d2 and the distance for t=2.5, d2.5, and D the difference. Then
D = d2.5 -d2
D= [44(2.5) -16(2.5²)]-[ 444(2) -16(2²)
= [88-64]-[110-100]
=24 ft.
Now, for the average velocity, we divide by the time.
v = D/t
= 24/.5
= 48 ft/s
Now for the second part:
We already have the number for d2; it's 24. So we just subtract that from d2.1
D = d2.1-d2
D = 44(2.1)-16(2.1²) -24
= 92.4-70.56 -24
= 2.16


Now, for the last part:
The velocity is this:
v = vo -32t
=44 -32(2)
= -20 ft/s
So, we know what we're looking for.
But the question says estimate:
So, the average velocity between d2 and d2.1 is this:
v = d/t
= 2.16/.1 = 21.6
So, since the velocity is increasing, we can say that the velocity at t=2 is a little less than the average. So, let's say about 20. :-)

Hope this helps.
FE

Answer 3

in spite of the reality which you probably did no longer specify,40t - 16t^2 is the equation of action -- its can grant the vertical place of the ball as a function of time. you are able to tell this by using fact the equation has a t squared dependence, which seems while an merchandise is decrease than the impact of a continuing tension, gravity to that end. by using fact the subject asks approximately elementary velocity, we choose an equation for velocity as a function of time; specifically the by-made from the equation of action. that is: 40 - 32t Now we choose the elementary fee of the era. the generic thank you to locate the elementary fee of a function over some era is to combine over that era, and then divide via the scale of the era. For .5, the era is going from 2 to 2.5, so V(avg) = (essential from 2 to 2.5 of 40 - 32 t) / .5 comparable is going for .a million, fairly now we are integrating from 2 to 2.a million and dividing via .a million. i've got faith that is organic accident that your first attempt labored out. Edit: I would desire to upload which you would be able to desire to apply the above guy or woman's technique besides, whether it in basic terms works to that end by using fact the value function is linear (relies upon in basic terms on t, no longer on t^2, t^3, etc.) The intergral technique is the suited and maximum generic thank you to locate the elementary fee of a function.

Answer 4

Estimate the instantaneous velocity when t = 2.

22 ft/sec