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
ad-work [718]
3 years ago
5

The acceleration of an object (in m/s^2) is given by the function a(t) = 9 sin(t). The initial velocity of the object is v(0) =

-11 m/s. a) Find an equation v(t) for the object velocity v(t) =___________b) Find the object's displacement (in meters) from time 0 to time 3 meters c) Find the total distance traveled by the object from time 0 to time 3 meters
Mathematics
1 answer:
pentagon [3]3 years ago
4 0

a) Acceleration is the derivative of velocity. By the fundamental theorem of calculus,

v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du

so that

v(t)=\left(-11\frac{\rm m}{\rm s}\right)+\int_0^t9\sin u\,\mathrm du

\boxed{v(t)=-\left(2+9\cos t)\right)\frac{\rm m}{\rm s}}

b) We get the displacement by integrating the velocity function like above. Assume the object starts at the origin, so that its initial position is s(0)=0\,\mathrm m. Then its displacement over the time interval [0, 3] is

s(0)+\displaystyle\int_0^3v(t)\,\mathrm dt=-\int_0^3(2+9\cos t)\,\mathrm dt=\boxed{-6-9\sin3}

c) The total distance traveled is the integral of the absolute value of the velocity function:

s(0)+\displaystyle\int_0^3|v(t)|\,\mathrm dt

v(t) for 0\le t and v(t)\ge0 for \cos^{-1}\left(-\frac29\right)\le t\le3, so we split the integral into two as

\displaystyle\int_0^{\cos^{-1}\left(-\frac29\right)}-v(t)\,\mathrm dt+\int_{\cos^{-1}\left(-\frac29\right)}^3v(t)\,\mathrm dt

=\displaystyle\int_0^{\cos^{-1}\left(-\frac29\right)}(2+9\cos t)\,\mathrm dt-\int_{\cos^{-1}\left(-\frac29\right)}^3(2+9\cos t)\,\mathrm dt

\displaystyle=\boxed{2\sqrt{77}-6+4\cos^{-1}\left(-\frac29\right)-9\sin3}

You might be interested in
Solve for x*<br> 55°<br> x + 74<br> I<br> 54°
tiny-mole [99]

The Answer Is 180. :)

8 0
3 years ago
The equation of line / is y=3x/a +5, where a is a positive constant. If the value of a in this equation is doubled, then the res
Anettt [7]

The resulting equation will represent a line whose slope is 1/2 times the slope of the line

<h3>How to determine the slope of the new line?</h3>

The equation of the line is given as:

y = 3x/a + 5

The constant a is a positive constant.

So, when the value of a in the equation is doubled, we have:

y = 3x/2a + 5

A linear equation is represented as

y = mx + b

Where m represents the slope.

So, we have:

m1 = 3/a

m2 = 3/2a

Substitute m1 = 3/a in m2 = 3/2a

m2 = 1/2 * m1

Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line

Read more about linear equation at:

brainly.com/question/14323743

#SPJ1

6 0
1 year ago
Family Video charges $10 for
Irina18 [472]

Answer:

4 movies, $20

Step-by-step explanation:

Given data

Family Video

charges $10 for a monthly membership and

$2.50 per movie

let the number of movies be x

and the charge for x movies be y

y= 10+2.5x----------1

Babe's  Movies

charges a $12

membership and $2 per

movie.

let the number of movies be x

and the charge for x movies be y

y= 12+2x----------2

equate 1 and 2

10+2.5x= 12+2x

collect like terms

12-10= 2.5x-2x

2= 0.5x

x= 2/0.5

x= 4 movies

put x= 4 in equation 1 or 2

y= 12+2x----------2

y= 12+2*4

y= 12+8

y= $20

4 0
3 years ago
A 32-oz. Can of spaghetti sauce cost $0.99. Find the unit per ounce to the nearest tenth of a cent.
Nostrana [21]
Jjjjjjjjjjjjjjjjjjjjjjjjjjjj
4 0
2 years ago
Read 2 more answers
Find the number of possible outcomes in the sample space.<br> You flip a coin once.
igor_vitrenko [27]
2 it will either land on heads or tails if you flip it once, hence 2 possible outcomes.
5 0
2 years ago
Other questions:
  • The lens equation is 1/f=1/p+1/q , where f is the focal length of the lens, p is the distance of the object from the lens, and q
    12·2 answers
  • The equation 2x2 – 5x = –12 is rewritten in the form of 2(x – p)2 + q = 0. what is the value of q?
    8·2 answers
  • Enter the fraction 1/5 as a decimal
    5·2 answers
  • The surface area of a square pyramid is found using the formula SA=b^2+2bh, where b is the length of the base and h is the heigh
    13·1 answer
  • Identify a counter example for the following conditional:
    14·1 answer
  • I don’t understand this can someone please give me and example on how to do it please?
    11·1 answer
  • The probability of choosing a green ball out of a box of balls is 2/9. What are the odds in favor of choosing a green ball?
    13·1 answer
  • Determining the End Behavior of a Polynomial Function HELP ASAP !!!!
    15·1 answer
  • What is the solution to the system of equations 3x + 5y = -1<br> ?<br> 6x - 4y = 26
    9·1 answer
  • If a rock falls from 125 feet, estimate how long it will take the rock to hit the ground. Estimate the square root to the neares
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!