Application of the Second Derivative (Acceleration)

Key Questions

• How do you find the acceleration for the function #s(t)=t^3+3t^2# ?

  Let us first find the velocity function #v(t)#.
  #v(t)=s'(t)=3t^2+6t#

  Let us now find the acceleration function #a(t)#.
  #a(t)=v'(t)=s''(t)=6t+6#

  Wataru · · Sep 14 2014
• What is acceleration?

  Answer:

  Acceleration is change in velocity over time #A=V/T#

  Explanation:

  For example lets say you have a car and its 0-60 MPH time is 3 seconds so the equation is #A=60/3# so you would take 60 and divide it by three and that is 20 so the 0-60 speed is 20 seconds.

  Spy Crab · 1 · Mar 6 2018
• How can I use derivatives to find acceleration, given a position-time function?

  Answer:

  Take the second derivative.

  Explanation:

  If you have a position function #x(t)#, then the derivative is a velocity function #v(t) = x'(t)# and the second derivative is an acceleration function #a(t) = x''(t)#.

  NJ · 1 · Apr 27 2018

• How do you find the acceleration for the function #s(t)=t^3+3t^2# ?
• How do you find the acceleration for the function #s(t)=-16t^2+100t +20# ?
• What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.0 m/s when going down a slope for 5.0s and how far does the skier travel in this time?
• A mass moves on a circular path of radius 2 m at constant speed 4m/s, what is the magnitude and direction of the average acceleration during a quarter of a revolution?
• How to find average acceleration? a bird is flying south at 8 m/s. the bird veers and changes velocity to 6 m/s east over a 2 second period. What is the average acceleration (magnitude and direction) during this 2 second interval?
• A particle moves according to the equation #s=1-1/t^2#, how do you find its acceleration?
• An object moves in such a way that when it has moved a distance s its velocity is #v=sqrts#, how do you find its acceleration?
• How do we use Rolle's Theorem to find whether function #f(x)=4x^2-8x+7# has a point where #f'(x)=0# in the interval #[-1,3]#?