Application of the Second Derivative (Acceleration)

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Questions

• 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]#?