Calculus 1

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 5. (Round your answers to two decimal places.)
f(t) = t^−1 − t

*We havent learned derivative yet but we have learned difference quotient and limits

  1. 👍 0
  2. 👎 0
  3. 👁 1,851
asked by TayB
  1. If all in one direction, the velocity is the speed.
    To get speed you need a speedometer.
    To get velocity you need a speedometer and a compass.

    If you knew derivatives this would be easy
    v = df/dt = -1 (t^-2) - 1
    = -1/t^2 - 1
    for t = 5
    v = -1/25 -25/25 = -26/25
    --------------------------
    if not then a mess as follows
    f(t+h) = 1/(t+h) -t -h
    f(t) = 1/t - t

    f(t+h) - f(t) = 1/(t+h)- 1/t -h
    = [ t -t - h ]/[t(t+h)] - h
    divide by h
    [ -1 ]/[t(t+h)] - 1
    let h---> 0
    -1/t^2 -1 like we said

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. Damon, where did you get the -h from?

    1. 👍 0
    2. 👎 0
    posted by TayB
  3. Damon, also how did you get f(t)=1/t -1? Shouldn't f(t)=1/t-t

    1. 👍 0
    2. 👎 0
    posted by TayB

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 9. f(t) = t ^-1 - t

    asked by Rob on February 24, 2010
  2. calculus

    A particle moves in a straight line with velocity given by v(t) =sin t metres per second. Find the total distance travelled by the particle in the first 4 seconds of motion

    asked by jenna on February 14, 2012
  3. math

    Which three options are true about motion in a straight line. A. A particle which moves at an increasing velocity has a constant acceleration. B. If two particles always have the same velocity as each other, their separation does

    asked by jojo on April 30, 2007
  4. calculus

    the displacement (in meter) of a particle moving in a straight line is given by the equation of motion s=5t^3+4t+2, where t is measured in seconds. Find the velocity of the particle at t=3.

    asked by L.J on November 17, 2011
  5. calculus

    velocity of a particle- the displacement s (in meters) of a particle moving in a straight line is given by the equation of motion s=4t^3+6t+2, where t is measured in seconds. Find the velocity of the particle s at times t=a t=1

    asked by Anonymous on May 16, 2015
  6. math

    The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 6/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.

    asked by Yuxiang Nie on February 21, 2019
  7. Math

    The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 4/t^2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.

    asked by Tay Tay on February 12, 2015
  8. maths

    Which three options are true about motion in a straight line. A. A particle which moves at an increasing velocity has a constant acceleration. B. If two particles always have the same velocity as each other, their separation does

    asked by kelly on April 18, 2007
  9. calculus 1

    particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 6. (Round your answers to two decimal places.) f(t) = t−1 − t velocity

    asked by monic on January 31, 2013
  10. Physics

    A charged particle is projected into a uniform B-field. Its velocity vector is perpendicular to the B-field vector. What type of path will the particle travel? Neglect gravity. Answer straight line motion elliptical motion

    asked by tom on July 16, 2013

More Similar Questions