The height of a ball thrown with a initial velocity of 64 ft and initial height of 6ft is given by the equation:
S(t)=-16t^2 + 64t + 6
Q:Find the average velocity from t=0 to t=2 second.
How I solve:
S'(2)=-32(2)+64
S'(2)=0
(S'(2)-S'(0))/2
Answer is (S(2)-S(0))/2
The professor told me the S'(t) is for velocity and S(t) is for finding height, so I use it for calculate the average velocity, but why the the anser use the S(t) equation?
When do I have to use S(t) or S'(t)?
+129850 S(t)=-16t^2 + 64t + 6 is the position function at anytime, t
The derivative of this is the velocity at anytime, t ......so....
S '(t) = -32t + 64
The average velocity = [change in velocity]/ [change in time]
So at t = 2 the velocity is -32(2) + 64 = 0
At t = 0 the velocity = -32(0) + 64
So....the average velocity is :
[ 0 - 64 ] / [ 2 - 0] = -64/2 = -32 ft/s
