1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What's the start speed and acceleration of the ball?

  1. Sep 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Using slant board, the ball was forced to move from bottom to the top. The ball was at the distance of 0.3 meters twice: after 1 and 2 seconds after start moving. What's the start speed and acceleration of the ball? (a=const)

    2. Relevant equations
    [tex]\newline x = x_0 + V_0*t + \frac{a*t^2}{2}[/tex]
    x₀ = 0 m
    V₀ = 0 m/s
    l = 0.3 m
    t₁ = 1 s
    t₂ = 2 s

    3. The attempt at a solution
    [tex]0.3 = 0 + V_0*1 + \frac{a*1^2}{2}[/tex]

    [tex]\newline 0.3 = 0 + V_0*2 + \frac{a*2^2}{2}[/tex]
    Here I can express, V₀. But I'm not sure the second expression is right. What's wrong?
     
  2. jcsd
  3. Sep 24, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    Re: Acceleration

    Hi Ockonal, welcome to PF.
    Your second expression is correct.
    Now subtract first equation from the second equation. You will get Vo in terms of a.
    Put it in the first equation to find a. Substitute this value in the second equation to get Vo.
     
  4. Sep 24, 2010 #3
    Re: Acceleration

    Oh, thanks.
     
  5. Sep 24, 2010 #4
    Re: Acceleration

    Okay, I did the job:

    [tex]0.3 = V_0 + \frac{a}{2}[/tex]
    [tex]0.3 = 2*V_0 + 2*a[/tex]
    =>
    [tex]V_0 = 0.3 - \frac{a}{2}[/tex]
    [tex]0.3 = 2*(0.3 - \frac{a}{2}) + 2*a[/tex]
    [tex]0.3 = 0.6 + a;[/tex]
    [tex]a = -0.3 (m/s^2)[/tex]
    [tex]V_0 = 0.3 - \frac{a}{2};[/tex]
    [tex]V_0 = 0.15 (m/s)[/tex]

    The questions are:
    Why the acceleration is negative? I think something is wrong in the first formulas.
    The start speed is 0.45 m/s (refer to the answers), the acceleration is right (0.3)
     
  6. Sep 25, 2010 #5

    rl.bhat

    User Avatar
    Homework Helper

    Re: Acceleration

    The acceleration is negative because the ball is moving up the inclined plane.
    Vo = 0.3 - a/2 = 0.3 - (- 0.3/2) = 0.3 + 0.15 = 0.45 m/s
     
    Last edited: Sep 25, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook