CALCULUS PLEASE HELP!!!

SHOW WORK PLEASE!!!
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 3 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period?
i) 1,2
ii) 1,1.1
iii)1,1.01
iv)1, 1.001

  1. 👍
  2. 👎
  3. 👁
  1. as you know, the average velocity is the integral divided by the time interval. Since the position is the integral of the velocity, the average velocity in [a,b] = (s(b)-s(a))/(b-a)

    So, we have

    i) (s(2)-s(1))/(2-1) = (2sin2π+3)-(2sinπ+3) = 0
    ii) (s(1.1)-s(1))/(1.1-1) = ((2sin1.1π+3)-(2sin.1π+3)))/.1 = -6.18034
    and so on

    1. 👍
    2. 👎
  2. a,b,c,d put all the value in the formula than divide the time :

    a) figure out s(2) and s(1) than divide

    s(2) = 3sin(pi*2) + 4cos(pi2) = 3(0) +4(1) = 4

    s(1) = 3sin(pi1) +4cos(pi1) = 3(0) +4(-1) = -4

    average velocity is ( s2-s1)/(2-1) = (4- (-4))/ 1 = 8 cm/s

    b) {s(1.1) -s(1)}/(1.1 -1) = -7.3 cm/s

    c) { s( 1.01)-s(1)}/(1.01-1) = -9.2 cm/ s

    d) {s(1.004)-s(1)}/(1.004-1) = -9.3

    e) take derivative then put t =1

    3picos(pit)-4pisin(pit)

    3picos(pi1)-4pisin(pi1)
    3pi(-1) = -3pi = -9.42 cm/s

    you can estimate t= 1 when they go small interval 1.0005 and so on they will approach to -9.4m/s bylooking

    note part b,c,d are the same part a, i just give you an answer but you have to work out like part a to show your works. you just punching in your calculator to figure out your answer by yourself

    1. 👍
    2. 👎
  3. s = 4 sin(πt) + 3 cos(πt)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A 59 g particle is moving to the left at 29 m/s. How much net work must be done on the particle to cause it to move to the right at 38 m/s? .....i have tried two different ways and gotten the wrong answer. Kinetic Energy = 0.5 *

  2. Calculus

    The position of a particle moving along the x-axis at time t > 0 seconds is given by the function x(t) = e ^ t - 2t feet. a) Find the average velocity of the particel over the interval [1,3]. b) In what direction and how fast is

  3. Calculus

    The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t − 7, 0 ≤ t ≤ 3 (a) Find the displacement. -7.5 m (b) Find the distance traveled by the particle during the given time

  4. math

    The acceleration of a particle at a time t moving along the x-axis is give by: a(t) = 4e^(2t). At the instant when t=0, the particle is at the point x=2, moving with velocity v(t)=-2. Find the position of the particle at t=1/2 if

  1. math

    The velocity function, in feet per second, is given for a particle moving along a straight line. v(t) = 3t − 2, 0 ≤ t ≤ 3 Find the displacement 15/2 Find the total distance that the particle travels over the given interval

  2. Calculus

    The velocity function is v(t)=t^2-5t+6 for a particle moving along a line. Find the displacement of the particle during the time interval [-3,6].

  3. Calculus

    The velocity function is v(t)=t^2−5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. So I found the antiderivative of the function, which

  4. Calculus

    The components of a position vector of a particle moving in the plane are components t cubed, 2 times the sine of t. What is the distance traveled by the particle from t = 1 to t = π? Type your answer in the space below and give

  1. physics

    Two forces, 1 = (3.85 − 2.85) N and 2 = (2.95 − 3.65) N, act on a particle of mass 2.10 kg that is initially at rest at coordinates (−2.30 m, −3.60 m). (a) What are the components of the particle's velocity at t = 11.8 s?

  2. Physics 221

    A 20g particle is moving to the left at 30 m/s. How much net work must be done on the particle to cause it to move to the right at 30 m/s. The answer is 0J of work, and i understand the method of equations, but i don't understand

  3. Calculus

    The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? b: What is the average velocity of the

  4. Physics

    A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c).

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