Results 1 to 8 of 8

Math Help - Kinematics Problem about catching up to a bus

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Kinematics Problem about catching up to a bus

    A student is running at her top speed of 4.6 m/s to catch a bus, which is stopped at the bus stop. When the student is still a distance 38.9 m from the bus, it starts to pull away, moving with a constant acceleration of 0.177 m/s^2.

    A) For how much time does the student have to run at 4.6 m/s before she overtakes the bus?
    I got 10.6s for this part by setting the distance equations for each to one another and solving for time.

    Then I'm not sure how to set up the rest...

    B) For what distance does the student have to run at 4.6 m/s before she overtakes the bus?

    C) When she reaches the bus, how fast is the bus traveling?

    D) What is the minimum speed the student must have to just catch up with the bus?

    E) For what time does she have to run in that case?

    F) For what distance does she have to run in that case?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,045
    Thanks
    886

    Re: Kinematics Problem about catching up to a bus

    Quote Originally Posted by ayyisei View Post
    A student is running at her top speed of 4.6 m/s to catch a bus, which is stopped at the bus stop. When the student is still a distance 38.9 m from the bus, it starts to pull away, moving with a constant acceleration of 0.177 m/s^2.

    A) For how much time does the student have to run at 4.6 m/s before she overtakes the bus?
    I got 10.6s for this part by setting the distance equations for each to one another and solving for time.

    Then I'm not sure how to set up the rest...

    B) For what distance does the student have to run at 4.6 m/s before she overtakes the bus?

    C) When she reaches the bus, how fast is the bus traveling?

    D) What is the minimum speed the student must have to just catch up with the bus?

    E) For what time does she have to run in that case?

    F) For what distance does she have to run in that case?
    you found t = 10.6 sec ...

    b) d_s = v_s \cdot t

    c) v_b = a_b \cdot t

    for parts d) , e), and f) , you'll need to find the student velocity v_s such that the graph of the student's position line is tangent to the bus' position curve. in other words, the student and bus are at the same position and both are traveling the same speed. therefore, solve the simultaneous system ...

    v_s \cdot t = 38.9 + \frac{1}{2}a_b t^2 and v_s = v_b = a_b \cdot t
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Re: Kinematics Problem about catching up to a bus

    For parts D-F, can I solve for v_s first then use that to solve for the next equation?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Re: Kinematics Problem about catching up to a bus

    Quote Originally Posted by skeeter View Post
    v_s \cdot t = 38.9 + \frac{1}{2}a_b t^2 and v_s = v_b = a_b \cdot t
    Is the second equation supposed to be like that or is it:

    v_s - v_b = a_b * t
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,045
    Thanks
    886

    Re: Kinematics Problem about catching up to a bus

    Quote Originally Posted by ayyisei View Post
    Is the second equation supposed to be like that or is it:

    v_s - v_b = a_b * t
    as i posted it ... I told you that the student's speed had to equal the bus' speed if he/she were to just catch it.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Re: Kinematics Problem about catching up to a bus

    Quote Originally Posted by skeeter View Post
    as i posted it ... I told you that the student's speed had to equal the bus' speed if he/she were to just catch it.
    So the t is t = 10.6 s that I found.
    The v_s is the constant velocity that the student is running at (4.6 m/s).
    The v_b is the velocity of the bus and the a_b its acceleration.

    I think I'll have to substitute v_s from the first equation into the second one?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,045
    Thanks
    886

    Re: Kinematics Problem about catching up to a bus

    Quote Originally Posted by ayyisei View Post
    So the t is t = 10.6 s that I found. incorrect ... it will be different because you're trying to find the minimum speed the student can run and just catch the bus.
    ...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Re: Kinematics Problem about catching up to a bus

    Oh okay. I understand what to do now. Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Kinematics problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: August 22nd 2009, 08:57 PM
  2. Kinematics problem
    Posted in the Advanced Applied Math Forum
    Replies: 8
    Last Post: June 16th 2009, 07:31 AM
  3. Catching a Bus
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 21st 2008, 12:30 PM
  4. speed - distance catching up
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 5th 2008, 08:50 AM
  5. kinematics problem.
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: October 17th 2007, 08:11 AM

Search Tags


/mathhelpforum @mathhelpforum