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!

Homework Help: Kinematics question (algebra)

  1. Aug 10, 2013 #1
    Hey guys so I have a quick question about the algebra for a question like this.
    I personally like to do the algebra first before I plug in the numbers so I have question for this one where it seems would be safer to plug in the numbers first?

    So won't be to tough,

    A book falls from a shelf that is 1.75m above the floor. How long will it take the book to reach the floor?

    So we have initial velocity = 0
    Displacement = 1.75m
    Acceleration/ gravity = 9.81m/s

    Its obvious that we can use the formula d=Vi(t)-1/2at^2

    So my question here is for the algebra if we plug the numbers in first it would be easier since we have initial velocity =0 so we can do (0)t=0. But if we didn't this is where I have trouble since I'm not the best at algebra, we'd get

    Square root( (2d/g)) - Vi(t) = t which confuses me because of the initial velocity * Time? What would we have to do with the time there.

    Thanks, I hope I didn't confuse anyone lol.
  2. jcsd
  3. Aug 10, 2013 #2


    User Avatar

    Staff: Mentor

    You should end up with a quadratic equation which you solve accordingly.

    Given your equation, d=Vi(t)-1/2at^2, you seem to be mixing up your coordinate directions. If the book is falling and you're taking the eventual displacement as positive (d = 1.75m), then your assumption is that "down" is positive. But then you write -1/2at2 which appears to assume that "up" is positive (given a positive value for acceleration).

    So. Let's say that "up" is positive, and the floor is the zero reference. Then the initial displacement is d and the final displacement is 0. Then you can write:

    ##0 = d + v_it - \frac{1}{2}at^2## {where a is a positive constant, the magnitude of the acceleration}

    There's your quadratic equation.

    Alternatively, you could take the zero reference to be at the book's initial position on the shelf, and "down" to be positive. Then you might write:

    ##-d = 0 + v_it + \frac{1}{2}at^2##

    In either case, if ##v_i## is zero then the quadratic becomes easy to solve...
  4. Aug 10, 2013 #3


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    If Vi ≠ 0, then you are dealing with a general quadratic equation in t. Use the quadratic formula to solve it. See here.

    For a video review, try here.

    [EDIT: I see gneill already provided an answer.]
  5. Aug 10, 2013 #4
    So, if the initial velocity is zero, you can just substitute Vi = 0 into your final equation and get the correct result. But seriously, for arbitrary initial velocity, if you want to solve it algebraically, it is best to follow the advice of the previous posters.
  6. Aug 10, 2013 #5
    Ah quadratic formula, been ages since I've used that, thanks a lot guys, it helped :)!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted