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Speed and acceleration

  1. Oct 12, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle moving along a straight line decelerates according to a= -kv, where k is a constant and v is velocity. If its initial velocity at time t=0 iv v0=4 m/s and its velocity at time t=2 s is v = 1 m/s, determine the time T and corresponding distance D for the particle speed to be reduced to one-tenth of its initial value

    ans T = 3.32 s, D = 5.19 M

    2. Relevant equations

    3. The attempt at a solution

    I have never tried a problem like this.. I just need some instruction on how to start.

    Thanks you very much!
  2. jcsd
  3. Oct 12, 2008 #2


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    Homework Helper

    Welcome to PF.

    Notice first your equation a = -kv expresses Acceleration as a variable in V.
    Hence to develop an equation expressing V as a function of t you will need to integrate a which is dv/dt. Rearranging your equation you have then:

    1/v*dv = -k*dt

    Integrating you get something of the form:

    ln|v| = -k*t + c

    You can use the values given to determine the constants of the equation.
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