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Acceleration and velocity involving calculus

  1. Sep 25, 2006 #1
    If the equation describing the motion of a rocket is
    x = 10 + 5t^2, write an expression for the instantaneous speed of the rocket. What is the instantaneous speed at 5 s. What is the acceleration?


    WHere do I begin? Do I need to take the integral anywhere?
     
  2. jcsd
  3. Sep 25, 2006 #2
    differentiate x = 10 +5t^2 with respect to t to get velocity and then differentiate your new velocity expression with respect to t to get the acceleration.

    Given your expression for x your acceleration is going to be a constant.
     
  4. Sep 25, 2006 #3
    Velocity
    x=10+5t^2
    Derivative with respect to t= 10t
    Instantaneous speed of rocket=10t

    Instantaneous speed at 5 s
    v=10t
    v=50 m/s
    Would this be in the correct units?

    Acceleration
    a=10
     
  5. Sep 25, 2006 #4
    yeah those are SI units so they are the correct units. Where the acceleration has units of [tex] \frac {m} {s^2}[/tex].
     
  6. Sep 25, 2006 #5
    So if I am understanding this correctly...

    The derivative of x=10+5t^2 with respect to t is the velocity
    Expression for instaneous speed of rocket
    V=10t

    Instantaneous speed at 5 s
    v=10t
    v=10(5)
    v=50 m/s

    Acceleration is the derivative of velocity (v=10t) with respect to t
    a=10
    a=10 m/s^2

    Look good?
     
  7. Sep 25, 2006 #6
    Yup that looks fine.
     
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