Results 1 to 4 of 4

Math Help - calculus help

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    1

    calculus help

    hi, i have some questions that i need help with i wondered if anyone could post the answers, here are the questions

    1. The distance moved by a car is given by the equation s=3tsquared-5t+2 using differentiation find an equation for the gradient of the tangent to the curve when the time is 2 seconds ie differentiate and evaluate.

    2. The velocity of a vibrating system can be modelled by the equation: v=5 sin 3t determine the equation for the rate of change of displacement with time (acceleration).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    I'm worried. These are the simplest possible applications of the derivative. I simply must question whether you have been paying attention in class. Perhaps you have been trying, but you have other distractions?

    In the first, can you find ds/dt of s'(t) or whatever it may have been called in your class or your textbook?

    You should get s'(t) = 6t - 5

    Can you reproduce that? What shall we do with that to solve the problem as it is stated?

    For the second, I have the same questions. Can you find dv/dt of v'(t) or whatever it may have been called in your class or your textbook?

    You should get v'(t) = 15*cos(3t)

    Can you reproduce that? What shall we do with that to solve the problem as it is stated?

    Honestly, you're going to have to do better than tripping over these two problems if you are going to survive this course of study.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    290
    1)s=3t^2-5t+2
    ds/dt=6t-5
    6t-5 is equation for finding slope at time t.
    at t =2
    ds/dt=7
    therfor slope at t=2 is 7
    2) acceleration is given by dv/dt where v is velocity
    since v=5sin3t therfor
    dv/dt=15cos3t which is equation of acceleration
    NOTE:acceleration is rate of change of velocity and velocity is rate of change of displacement.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1
    Quote Originally Posted by tom555 View Post
    hi, i have some questions that i need help with i wondered if anyone could post the answers, here are the questions

    1. The distance moved by a car is given by the equation s=3tsquared-5t+2 using differentiation find an equation for the gradient of the tangent to the curve when the time is 2 seconds ie differentiate and evaluate.

    2. The velocity of a vibrating system can be modelled by the equation: v=5 sin 3t determine the equation for the rate of change of displacement with time (acceleration).
    1.
    s=3t^2 - 5t + 2
    \frac{\mathrm{d}s}{\mathrm{d}t} = 6t - 5
    You are told to find the gradient of the tangent at t=2 therefore:
    \frac{\mathrm{d}s}{\mathrm{d}t} = 6(2) - 5 = 7


    2.
    v = 5 \sin 3t
    a = \frac{\mathrm{d}v}{\mathrm{d}t} = \frac{\mathrm{d}^2x}{\mathrm{d}t^2}
    a = \frac{\mathrm{d}(5 \sin 3t)}{\mathrm{d}t} = 15 \cos 3t
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 13th 2011, 09:11 PM
  2. Replies: 2
    Last Post: June 25th 2010, 10:41 PM
  3. Replies: 1
    Last Post: February 11th 2010, 07:09 AM
  4. Calculus III But doesn't require Calculus :)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 19th 2009, 04:23 PM
  5. Replies: 1
    Last Post: June 23rd 2008, 09:17 AM

Search Tags


/mathhelpforum @mathhelpforum