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
marissa [1.9K]
3 years ago
9

The acceleration, in feet per second per second, of an object is given by the acceleration function a(t)=2 sin t+1. The initial

velocity is v(0)=0 and the initial position is s(0) =3. Find the equation of velocity function. Find the position function and the average value of the position function from time t = 2 seconds to t = 5 seconds. Show all your work.

Mathematics
2 answers:
Simora [160]3 years ago
7 0

Answer:

velocity v(t) = -2cos(t)+t+2

position s(t) = -2sin(t)+\frac{t^2}{2} +2t + 3

average of position from 2 to 5 = 17.666

Step-by-step explanation:

velocity is anti-derivative/integral of acceleration

\int{(2sin(t)+1)} \, dt = -2cos(t)+t+C

v(0) = 0

0 = -2cos(0)+0+C = -2 +C; C = 2

v(t) = -2cos(t)+t+2

position is anti-derivative of velocity

\int{(-2cos(t)+t+2)} \, dt = -2sin(t)+\frac{t^2}{2} +2t + C

s(0) = 3

3 = -2sin(0) + 0 + 0+ C

3 = C

s(t) = -2sin(t)+\frac{t^2}{2} +2t + 3

average value of a function of a domain [a, b] is given by the equation

\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx

average of position from t = 2 to t = 5

\frac{1}{5-2} \int\limits^5_2 {(-2sin(t)+\frac{t^2}{2} +2t + 3)} \, dt

\int\limits^5_2 {(-2sin(t)+\frac{t^2}{2} +2t + 3)} \, dt = 2cos(5)+125/6+25+15 - 2cos(2) - 8/6 -4 + 6

=52.999 (use a calculator)

52.999/3 = 17.666

Harrizon [31]3 years ago
7 0

Answer:

v(t) = v(t) = -2cos(t) + t + 2

s(t) = -2sin(t) + ½t² + 2t + 3

Average value of s: 17.0 (3 sf)

Step-by-step explanation:

v(t) is the integral of a(t)

v(t) = -2cos(t) + t + c

t = 0, v = 0

0 = -2 + 0 + c

c = 2

v(t) = -2cos(t) + t + 2

Displacement/position is the integral of v(t)

s(t) = -2sin(t) + ½t² + 2t + c

t = 0, s = 3

3 = 0 + 0 + 0+ c

c = 3

s(t) = -2sin(t) + ½t² + 2t + 3

Integral of s:

2cos(t) + ⅙t³ + t² + 3t + c

Average value

= 1/(b - a) × integral

= 1/(5-2) × [ (2cos(5) + ⅙(5)³ + 5² + 3(5) + c) - (2cos(2) + ⅙(2)³ + 2² + 3(2) + c) ]

= ⅓[61.4006577 - 10.50103966]

= 16.96653935

You might be interested in
1. What is the standard form for the<br> following:<br> 3x^2 - 4x + 6x^5 + 10x^3 - 8
Mrrafil [7]

Answer:

how this helps

Step-by-step explanation:

6 0
3 years ago
Which addition expression
marin [14]
The correct answer is B. If you drop the parenthesis and collect like terms you get 8-3i.
3 0
3 years ago
Read 2 more answers
What is the length of BD?
Ket [755]

Answer: BD = 9 units

Step-by-step explanation:

ABQ and CDQ are congruent triangles. That means their angle measures are the same but their lengths may be proportional.

19.2 / 32 = 0.6

15 * 0.6 = 9

So the length of side BD is 9 units.

4 0
4 years ago
Read 2 more answers
Find the length of the hypotenuse
Darina [25.2K]

Answer:

The Hypotenuse is side just opposite to the right angle.

Step-by-step explanation:

By Pythagoras' theorem,

c^2=a^2+b^2

c^2(hypotenuse to be found)= 30^2+ 16^2

<em>c^2=1156 </em>

<em><u>Therefore, c ( i.e. the hypotenuse) will be the square root of 1156. </u></em>

<em><u>The square root of 1156 is 34. </u></em>

<h2><em><u>Thus, c ( hypotenuse) = 34</u></em></h2>

Hope it helped :)

3 0
3 years ago
Determine whether the given value is a solution of the equation. 36 = k 6 ; k = 6 6 a solution of 36 = k 6 .
Mila [183]

Answer:

Yes: the variable K would equal "6"

Step-by-step explanation:

After you set you equation up, you have to isolate the given variable. To do that you have to do the recipriocal (6k-multiplying) which would be division. You would divide k = 36 ÷ 6 . that isolates the variable ,which you would then solve. k = 6 .

4 0
4 years ago
Other questions:
  • Megan hiked 15.12 miles in 6.3 hours. If Megan hiked the same number of miles each hour , how many miles did she hike each hour?
    14·1 answer
  • Simplify the expression. 9r 3r2 – 5r 7
    10·2 answers
  • In triangle RXT A 51 B42 C39 or D5
    7·1 answer
  • The average yield of the standard variety off soybeans per acre on a farm in a region is 48.8 bushels per acre, with a standard
    13·1 answer
  • Solve eqaution 22p+11=4p-7
    12·2 answers
  • Which set of data contains two outliers?
    12·1 answer
  • The figure below shows segments KL and MN which intersect at point P. Segment KM is parallel to segment LN:
    5·2 answers
  • Please help me with this IXL problem
    14·2 answers
  • I need help with this .<br>use the name of the graph to name the function ​
    10·1 answer
  • Is -4.9 bigger or smaller then 3.6
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!