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!

Deriving v and a from a x(t)-function

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi again folks! I just need confirmation on this, since I'm quite sure I've got it right. Anyway here it goes.

    The position of a particle is given by the function x(t)= A + Bt + Ct² + Dt³. The values of the constants are the following: A= 4,0; B=2,0; C= -3 and D=1,0.
    a) Give the units of the constants if [x]=m and [t]=s
    b) What is the velocity and acceleration at t=3s?
    c) Give an expression for the velocity v=v(t) and make a sketch for the time interval 0 to 3s
    d) From the graph, give the acceleration at t=1s
    e) Compute the acceleration at t=1s by examining the quota delta t / delta v for the time intervals delta t= 1,0s; 0,5s; 0,1s and 0,001s

    2. Relevant equations

    3. The attempt at a solution
    a) since [x]=m and [t]=s, then [A]=m, = ms[tex]^{-1}[/tex], [C]= ms[tex]^{-2}[/tex] and [D]= ms[tex]^{-3}[/tex]
    b) I differentiate once to get the expression for v, v=dx/dt = 3Dt² + 2 Ct + B which gives the instantaneous velocity (perhaps speed in this case) as 11 m/s. Differentiate a second time to get a, a=d²x/dt²= 6Dt + 2C which gives the acceleration at t=3s to be 12m/s²
    c) The expression of v I got to be this (taking the constants into account) v= v(t) = 3t² - 6t + 2. this gives a parabola (or part of one) with its apex at v = -1 at t=1. So, the acceleration would be 0 m/s².
    d) With limiting function and the given time intervals a approaches zero as delta t approaches zero

    I'd really like confirmation on this one :) Thanks!
  2. jcsd
  3. Sep 1, 2010 #2


    User Avatar
    Homework Helper

    They look correct to me.
  4. Sep 1, 2010 #3
    Thank you :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Deriving v and a from a x(t)-function
  1. V(t) and x(t) (Replies: 1)