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Determine Velocity at each second

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data
    A ball is thrown straight up at 30m/s. Assume g is 10m/s/s Show the dispacement, velocity, and acceleration at each position.


    2. Relevant equations
    Vf² = Vi² + 2aΔx
    Vf = Vi + at


    3. The attempt at a solution
    So first I wanted to solve for the time it takes to go up so

    Vf = Vi + at
    0 = 30 + (-10)t
    t = -30/-10 = 3 seconds up
    then just times 2 because its the same coming down
    so 6 seconds in all

    Now for distance up

    Vf² = Vi² + 2aΔx
    Δx = (Vf² - Vi²)/2a
    Δx = (0 - 900)/2(-10)
    Δx = (-900)/(-20)
    Δx = 45m up
    and again times 2
    so 90 meters in all

    Now for some reason I'm having trouble figuring out how to find the velocity,displacement,and acceleration at each 1 second interval.

    Should acceleration stay the same until the top where its 0 then change to +10m/s/s?

    And how and what formula would I use for the other two?

    Thanks in advance everyone
     
  2. jcsd
  3. Feb 6, 2013 #2
    Hint: For the velocity simply tabulate Vf = Vi + a*t. On the way up, a is negative. Use results for Vf in your first equation and solve for delta X. Repeat.
     
  4. Feb 6, 2013 #3
    Thanks Lawrence ...I kept thinking I had to bring in another formula. Thanks again!
     
  5. Feb 6, 2013 #4
    Actually ....when solving for acceleration ....I get that on the way up its negative ....but by using something using my results from above...
    Vf = Vi + at
    (Vf-Vi)/t

    Using say
    V(0)=30m/s and V(1)=20m/s
    So
    (20-30)/1 = -10 which I assumed

    But

    Using V(4) and V(5)

    (-20 - (-10))/1
    That comes to -10 as well...but shouldnt acceleration be positive at this time?
     
  6. Feb 7, 2013 #5
    If you choose the starting point to be the velocity at the highest point where it is zero and let downward velocities be positive, then you will get a positive acceleration.

    The equation Vf = Vi + at enables one to determine a velocity at a later time under constant acceleration over that time period. If the acceleration is in the same direction as the velocity and velocity is positive, acceleration is positive. Vice versa is also true. If you use it to determine accelerations, the sign of the acceleration is dependent on the sign convention you choose for the velocities. If the magnitude of the velocity increases, the acceleration has the same sign as the velocity. If magnitude of velocity decreases, acceleration has the opposite sign.
     
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