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Differental / Vector problem

  1. Oct 21, 2008 #1
    My book says V=dx/dt=B+3Ct^2 when x=A+Bt+Ct^3. This doesn't make any sense to me? Could anybody explain how x/t turned into B+3Ct^2 ?

    a=dV/dt=6Ct How can V/t turn into 6Ct ? I don't understand this either :( If anobody could explain this would help me really really much.
  2. jcsd
  3. Oct 21, 2008 #2
    V is the rate of change of position, so you would have to take the derivative of x to get V, let's take the derivative of each component, dx/dt = (d/dt)A + (d/dt)Bt + (d/dt)Ct^3
    A is a constant, therefore the derivative of A would become zero.
    The derivative of anything in the form of Dt^n would equal Dnt^(n-1), so the derivative of Bt would equal B(1)t^(1-1), which simplifies to B
    And the derivative of Ct^3 would equal C(3)t^(3-1), which simplifies to 3Ct^2
    And when you put it all together you get, V = B + 3Ct^2

    to find acceleration, you just take the derivative of velocity.
    dv/dt = (d/dt)B + (d/dt)3Ct^2
    The derivative of B, a constant, would be zero, and the derivative of 3Ct^2 would be 3(2)Ct^(2-1), which would simplify to 6Ct
    So acceleration equals 6Ct

    hope this helps
  4. Oct 21, 2008 #3
    Thank you very very much!
    Now I actually understand what I'm doing =)

    Tommorow I'm going to study kinematics of spinning motion, hope I won't have trouble there!
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