AP Calculus

posted by .

The position of a particle moving on the x-axis at time t>0 seconds is: x(t)= e^t - t^1/2.

a) Find the average velocity of the particel over the interval [1,3].

b) In what direction and how fast is the particle moving at t= 1 seconds?

c) For what values of t is the particle moving to the right?

d) Find the postition of the particle when its velocity is 0.

  • AP Calculus -

    a) Calculate the change in x from t=1 to t=3 and divide by 2 s for athe anverage velcoity

    b) Calculate dx/dt at t=1
    velocity = dx/dt = e^t - (1/2)/t^1/2

    c) Find out when dx/dt > 0 . That will be the answer. You may need to graph dx/dt

    d) Solve for t when dx/dt = 0
    Use that t in the x(t) equation.

    These are exercises you should be able to do yourself. Someone will gladly critique your work.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus III

    A particle is moving in R2 according to the law x=t^2, y=t^3 (time is measured in seconds, coordinates in meters). (a) What is the average velocity of the particle over the time interval [1,1.1]?
  2. physics

    In this problem you will determine the average velocity of a moving object from the graph of its position as a function of time . A traveling object might move at different speeds and in different directions during an interval of time, …
  3. calculus

    let f(t) = 2*pi*t + sin(2*pi*t) a) find value of t in open interval (0,2) for which the tangent line at (t, f(t)) is parallel to the line through (0,0( and (2, 4pi) b) suppose the given funtion describes the position of a particle …
  4. Calculus

    At time t >or= to 0, the position of a particle moving along the x-axis is given by x(t)= (t^3/3)+2t+2. For what value of t in the interval [0,3] will the instantaneous velocity of the particle equal the average velocity of the …
  5. calculus

    5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5?
  6. calculus

    A particle is moving along the x- axis so that its velocity at any time t ≥0 is give by v(t) = (2 pi - 5)t - sin(pi t) A. Find the acceleration at ay time t. B. Find the minimum acceleration of the particle over the interval …
  7. Calculus

    The displacement (in meters) of a particle moving in a straight line is given by s=2t^3 where is measured in seconds. Find the average velocity of the particle over the time interval [10,13]. the average velocity is 798 What is the …
  8. 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?
  9. calculus

    A particle moves on a line so that its position at time t seconds is p(t)=3t3 meters to the right of the origin. Find the time c in the interval (4,8) for which the velocity of the particle at time c is equal to the average velocity …
  10. Calculus

    Sorry this is really long. Just wondering how I would do each of these A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between …

More Similar Questions