1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lara [203]
3 years ago
9

The position function of an object moving along a straight line is given by s=f(t). The average velocity of an object over the t

ime interval [a,b] is the average rate of change of f over [a,b]; it’s velocity at t=a is the rate of change of f at a.
A ball is thrown straight up with an initial velocity of 144ft/sec, so that it’s height (in feet) after t sec is given by s=f(t)= 144t-16t^2.
(A)What is the average velocity of the ball over the following time intervals?
[3,4]= ft/sec
[3,3.5]= ft/sec
[3,3.1]= ft/sec

(B) what is the instantaneous velocity at time t=3? Ft/sec

(C) what is the instantaneous velocity at time t=8? Ft/sec

(D) when will the ball hit the ground?
Mathematics
1 answer:
Oksana_A [137]3 years ago
3 0
A) Position at time t = 3 s : 
<span>s₁ = 144×3 - 16×3² = 288 ft </span>
Position at time t = 4 s : 
<span>s₂ = 144×4 - 16×4² = 320 ft 
</span>
<span>Δs = s₂ - s₁ = 320 - 288 =  32ft </span>
<span>Δt = t₂ - t₁ = 4 - 3 = 1 s 

</span><span>Vavg[3, 4] = Δs / Δt = 32 / 1 = <u>32 ft/s</u>
</span><span>Vavg[3 , 3.5] = [(144×3.5 - 16×3.5²) - (144×3 - 16×3²)] / [3.5 - 3] = <u>40 ft/s</u>
</span><span>Vavg[4 , 4.1] = [(144×3.1 - 16×3.1²) - (144×3 - 16×3²)] / [3.1 - 3] = <u>4.64 ft/s</u></span>

B) lim [(144t - 16t²) - (144×4 - 16×3²)) / (t - 3)] = 
<span>t→3
</span>lim [(-16t² + 144t - 288) / (t - 3)] = 
<span>t→3
</span>
<span><u>48 ft/s</u>

</span>C) <span>lim [(144t - 16t²) - (144×8 - 16×8²)) / (t - 8)] = </span>
<span>t→8 </span>

<span>lim [(-16t² + 144t - 128) / (t - 8)] = </span>
<span>t→8 </span>

<span>lim (-16t + 16) = </span>
<span>t→8 </span>

<span><u>-112 ft/s</u> 

D) </span><span>144t - 16t² = 0 </span>
<span>(144 - 16t) t = 0 </span>
<span>t = 0 </span>
<span>or </span>
<span>144 - 16t = 0 
</span>
<span><u>t = 9 </u></span>
You might be interested in
-2 1/4 - ( - 3/4) =<br>​
Grace [21]

Answer: -1.5

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Find the area of a circle whose circumference is 24 pi.
lozanna [386]

Answer:

452.39 sq.unit is the area of that circle.

6 0
3 years ago
Solve the following numerical problems. a. If a bus travels 6 km in 10 minutes, what distance does it travel in 1 secon
Alex17521 [72]

Answer:

10 meters

Step-by-step explanation:

6 0
2 years ago
I have 256 fence and the lengths are 3 times it's width. What are the lengths ?
Montano1993 [528]
If this is a rectangle, then the answer is the length=96 unitsI just formed two linear equations that follow the information. 
1. 2l + 2w= 256
2. l=3w
Then, I solved for w by using substitution. w is 32. I then multiplied it by 3. I get the length as 96. 
6 0
3 years ago
Can someone also help me on this one!!
alexdok [17]

The change in the X values is in multiples of 2.

The change in the h(x) values need to be: -0.3 x 2 = -0.6

Now find the h(x) values that have a difference of -0.6

A negative value is a decrease.

2 to 4 is an increase.

4 to 6 is an increase.

6 to 8 is an increase.

8 to 10 is an increase.

10 to 12 = 20-19.8 = 0.2

12 to 14 = 19.8 - 19.2 = 0.6

The two columns are 12 and 14

5 0
3 years ago
Other questions:
  • F(x)=x^-2x+4 find f(-1)
    7·1 answer
  • What is the exact value of 11.68 - 0.48 ÷ (-1.6) =
    10·2 answers
  • What’s the area of a regular pentagon with a side length of 4 meters ?
    15·1 answer
  • What is 1million to the 10th power
    13·2 answers
  • &lt;a and &lt;b are complementary angles. The measure of &lt;a is four times as big as &lt;b. What is the measure of &lt;a​
    7·1 answer
  • Convert 2x + 37y = 18 to point-slope form.
    7·1 answer
  • Help im on a meeting this need to be done
    10·1 answer
  • Please help time crush 15 points!
    13·1 answer
  • The scale of a map is 1:50000. A lake on the map is 6.16cm². find the actual area of the lake in hectares.
    9·1 answer
  • Over what interval is the function in this graph constant
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!