Results 1 to 4 of 4

Math Help - [SOLVED] derivative (problem solving)

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    151

    [SOLVED] derivative (problem solving)

    Let s = s(t) be the position function of a particle moving in a straight line.
    Suppose that the position of the particle is given by the formula
    s (t) = t^2 e^-t ; t >= 0
    where t is measured in seconds and s in meters.

    (i) Find the velocity of the particle at time t.
    * should i differentiate s(t) to get the velocity?

    (ii) When is the particle at rest?
    * when velocity = 0.. am i right?

    (iii) Find the total distance traveled by the particle during the first two seconds.
    *dont have any idea..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Dec 2009
    Posts
    19
    Quote Originally Posted by nameck View Post
    Let s = s(t) be the position function of a particle moving in a straight line.
    Suppose that the position of the particle is given by the formula
    s (t) = t^2 e^-t ; t >= 0
    where t is measured in seconds and s in meters.

    (i) Find the velocity of the particle at time t.
    * should i differentiate s(t) to get the velocity?

    (ii) When is the particle at rest?
    * when velocity = 0.. am i right?

    (iii) Find the total distance traveled by the particle during the first two seconds.
    *dont have any idea..
    You're right about parts i and ii. For iii, simply let t = 2 in the original equation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    151
    (i) Find the velocity of the particle at time t.
    * should i differentiate s(t) to get the velocity?

    answer--> (2t e^-t) - (t^2 e^-t)

    (ii) When is the particle at rest?
    * when velocity = 0.. am i right?

    answer-->
    (2t e^-t) - (t^2 e^-t) = 0
    (2t e^-t) = (t^2 e^-t)
    (2e^-t) = (t e^-t)
    *how to solve t?

    (iii) Find the total distance traveled by the particle during the first two seconds.
    *dont have any idea..

    at t = 2
    s (t) = t^2 e^-t
    s (2) = 2^2 e^-2
    .......= 0.54 meters

    is my answer for (i) and (iii) is correct?
    how am i going to solve (ii)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2009
    Posts
    19
    Quote Originally Posted by nameck View Post
    (i) Find the velocity of the particle at time t.
    * should i differentiate s(t) to get the velocity?

    answer--> (2t e^-t) - (t^2 e^-t)

    (ii) When is the particle at rest?
    * when velocity = 0.. am i right?

    answer-->
    (2t e^-t) - (t^2 e^-t) = 0
    (2t e^-t) = (t^2 e^-t)
    (2e^-t) = (t e^-t)
    *how to solve t?

    (iii) Find the total distance traveled by the particle during the first two seconds.
    *dont have any idea..

    at t = 2
    s (t) = t^2 e^-t
    s (2) = 2^2 e^-2
    .......= 0.54 meters

    is my answer for (i) and (iii) is correct?
    how am i going to solve (ii)?
    Your answers for i and iii are correct. For ii try the following:

     2t e^{-t} - t^2 e^{-t} = 0

    Take out a factor of  e^{-t} :

     e^{-t} (2t-t^2) = 0

    Now, for this to be true, either  e^{-t} = 0 , or  2t-t^2 = 0

    One of the properties of the exponential function is that it is NEVER equal to zero, hence the latter must be true:

     2t-t^2 = 0

    Can you solve this?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving problem using derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 9th 2011, 04:19 AM
  2. solving problem using definition of derivative
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 16th 2010, 08:14 AM
  3. [SOLVED] first derivative set to 0 solving
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 28th 2010, 02:54 PM
  4. [SOLVED] Need help solving a problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 19th 2009, 12:58 PM
  5. [SOLVED] Problem Solving
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: February 3rd 2009, 03:40 PM

Search Tags


/mathhelpforum @mathhelpforum