Math/ Calculus Please HELP!!!

posted by .

The following table gives the velocity v(t) (in feet per sec) at different instances of time t (in sec) of a particle moving along a horizontal axis.

t 0 4 8 12 16 20
v(t) 43 42 40 35 25 5

Estimate the distance traveled by the particle between t = 0 sec and t = 20 sec using 5 time intervals of equal length with

(a) left endpoints
Estimated distance = _____feet

(b) right endpoints
Estimated distance = _____feet

  • Math/ Calculus Please HELP!!! -

    t 0 4 8 12 16 20

    vt 43 42 40 35 25 5

  • Math/ Calculus Please HELP!!! -

    left endpoints: 4*43 + 4*42 + ... + 4*25
    right ends: 4*42 + 4*40 + ... + 4*5

  • Math/ Calculus Please HELP!!! -

    hey thanks but i still don't get how you arrived to this answer?

  • Math/ Calculus Please HELP!!! -

    consult your text, or do a web search. To approximate the area under a curve, draw rectangles of (in this case) width 4.

    The vertical sides intersect the curve at various points. To approximate using left endpoints, make the height of the rectangle spanning x0-x1 the value of f(x0) - the left height.

    Thus, the area of rectangle from xi to xi+1 is w*f(xi)

    Using the right endpoints of the intervals, the area is w*f(xi+1)

    Takes a lot of words, but any illustration should make it clear.

    Why are we approximating the area under the curve? Because we are given the speed at various times. speed is the derivative of the position. The position is thus the integral of the speed over an interval.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    I don't understand what the graph is suppose to show and what the integral equation is suppose to mean. How would I use the graph to answer the questions?
  2. calculus

    The velocity of a particle moving along the t-axis is given by f(t)=2+.05t cm/sec. Use a graph of y=f(t) to find the exact change in position (distance traveled) for the particle from t=2 to t=8.
  3. physics help

    The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time …
  4. physics help

    The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time …
  5. Calculus PLEASE check my work ,

    1.) which of the following represents dy/dx when y=e^-2x Sec(3x)?
  6. Calculus

    The velocity of a particle moving along the x-axis is given by f(t)=6-2t cm/sec. Use a graph of f(t)to find the exact change in position of the particle from time t=0 to t=4 seconds.
  7. Calculus

    Solve: The posistion of a particle moving along a coordinate line is s=sqrt(5+4t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec. A) 2/3 m/sec B) 4/3 m/sec C) -1/3 m/sec D) 1/6 m/sec Thank you!
  8. calculus

    Me again. One last question! Again, just needed my answer verified with any explanation or walk-through. The position of a particle moving along a coordinate line is s=√(3+6t) with s in meters and t in seconds. find the particle's …
  9. Math 160

    The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at …
  10. Calculus Answer Check

    A particle moves along a line so that its position at any time t >= 0 is given by the function -t^3 + t^2 + 5t + 3, where p is measured in feet and t is measured in seconds. 1. Find the displacement during the first four seconds. …

More Similar Questions