i did this problem and it isn't working out, so i think i'm either making a mistake or misunderstanding what it's asking.

A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given by v(t) = 1 - sin(2pi*t).

a. Acceleration a(t) of the particle at any time t?

i said that acceleration was the derivative of velocity, so i took the derivative of the velocity function.

v(t) = 1 - sin(2pi*t)
v'(t) = -cos(2pi*t) x 2pi
a(t) = -2pi*cos(2pi*t)

b. Values of t between 0 and 2 where the particle is at rest?

i said it was at rest when velocity = 0.

0 = 1 - sin(2pi*t)
1 = sin(2pi*t)

sin(pi/2) = 1, so...
2pi*t = pi/2
4pi*t = pi
4t = 1
t = 1/4

c. Position x(t) of the particle at any time t if x(0) = 0?

i didn't understand the part about x(0) = 0. i kind of ignored it and it didn't work out. i figured that the position function was the anti-derivative of the velocity function and did:

anti-derivative of 1 - sin(2pi*t)
1/2pi x anti-derivative of 1 - sin(2pi*t)
1/2pi (t + cos(2pi*t)) = x(t)

but that doesn't equal 0 when t = 0. help?

  1. 👍
  2. 👎
  3. 👁
  1. in b) you were right to find
    t = 1/4
    but remember the period of 1 - sin(2pi*t)
    is 2pi/2pi = 1

    so another solution would be 1/4 + 1 or
    t = 5/4

    so the times between 0 and 2 when the object is at rest is
    t = 1/4 and t = 5/4

    for c) if
    v(t) = 1 - sin(2pi*t)
    then x(t) = t + (1/2pi)cos(2pi*t) + c
    but you were given x(0) = 0
    0 = 0 + (1/2pi)cos(0) + c
    0 = )1/2pi) + c
    c = -1/(2pi)

    so x(t) = t + (1/2pi)cos(2pi*t) - 1/(2pi)

    1. 👍
    2. 👎
  2. omg i can't believe i just forgot c in part c. it's even called part c!

    and thank you for the help with part b. i completely forgot about that!

    1. 👍
    2. 👎
  3. Let R be the region bounded by the y-axis and the graph of y=xcubed divided by 1+xsquared and y=4-2x,as shown inthe figure above.

    find the area of R

    find the volume of the solid generated when R is revolved about the x-axis

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    If the equilibrium concentrations are [PCl5] = 1.0M, [Cl2] = 0.10M, what is the equilibrium constant value? PCl5(g) PCl3(g) + Cl2(g) Would you mind showing the calculations Please. I've been working on this problem over an hour

  2. Math 10

    A trundle wheel can be used to measure the walking distance between two locations. a) If the diameter of a trundle wheel is 45 cm, how far will a person have walked when the wheel makes one full rotation? b) If a person walks for

  3. DESPERATE NEED OF HELP--Chemistry, almost done

    Calculating Yield--need some help finishing problem. Almost done, just need help one ONE step, please help!!? Well we did a lab on limiting reagent/reactants. The balanced equation is Sr(NO3)2 + 2KIO3 --> Sr(IO3)2 + 2KNO3 Mols of

  4. Trig

    Find an equation for the hyperbola described. Foci at (-4,0) and (4,0); asymptote the line y= -x. Please explain the steps of this problem. My book does not get an example of this type of problem and I'm not having any luck

  1. History

    What were the early effects of the Industrial Revolution on the working class? 1)Members of the working class enjoyed shorter working hours and better living conditions. 2)The working class obtained greater opportunities for

  2. English

    1. To come up with possible solutions to a problem is referred to as: A. decision making. B. concept mapping. C. critical thinking. D. problem solving. is it D 2. "Should I apply for a job or go for an internship?" is an example

  3. Human Relations, Part 1

    Which of these statements is true? A. Waste isn't a problem in reaching group goals. B. Sacrifice isn't necessary to achieve group goals. C. Individual productivity is necessary for group productivity. D. Individual productivity

  4. Pre Calc

    use properties of the trigonometric function to find the exact value of each expression. Do no use a calculator. sec ( - pi/18) * cos (37 pi)/18 I do not see how to do this problem. Every time I do it out I get a reference angle

  1. Designing Specialty Areas

    Which of the following would meet the criteria discussed in the textbook for a one-portion recipe for kindergarten children? A. Making individual brownies B. Making a loaf of banana bread from a mix C. Making individual fruit

  2. math

    27x^3+8 27 isn't a perfect square so I'm not sure how to go about this problem?

  3. Math/Vectors

    I need help on a homework problem. "Determine a vector equation for the line perpendicular to 4x-3y=17 and through point (-2,4). The answer in the book is given as [x,y]=[-2,4]+t[-4,3].Isn't the normal to the scalar equation

  4. Geometry

    In Triangle XYZ, the measure of angle X is 5/8 as large as the measure of angle Y. If the measure of angle Z is 1/4 as large as the measure of the angle Y, what's the measure of all three angles. I've tried making up numbers to

You can view more similar questions or ask a new question.