Chapter 20 - 4  Velocity and Acceleration
 
Where "s" is the position at any time "t"
 
 
 
Comments
v(t) = 0 means the object is not moving.
v(t) = 3 means the object would be moving forward (positive)
v(t) = -2 means the object would be moving backward (negative)
a(t) = 0 means there is no change in the velocity
a(t) = 5 means the object is going faster (positive)
a(t) = -3 means the object is slowing down.
 
Sample problems
 
v(t) = s'(t) = 6t2 + 5
a(t) = v'(t) = 12t
v(2) = 6(4) + 5 = 29
a(2) = 12(2) = 24
 
48 = 128 - 32t          16 = 128 - 32t          -48 = 128 - 32t
                      -80 = -32t                -112 = -32t               -176 = -32t

                        2.5 = t                        3.5 = t                       5.5 = t

0 = 128 - 32t
-128 = -32t
4 = t
s(4) = 128(4) - 16(16) = 512 - 256 = 256'
128t - 16t2 = 0
16t(8 - t) = 0
At t = 0, or t = 8.  Think.  At t = 0, you haven't thrown the ball yet!  The ball will hit the ground in 8 seconds.  You could have reasoned that it took 4 seconds to reach maximum height and another 4 secs to come back down.
a(t) = -32 ft/sec2
No matter what time it will always be -32. (This is the effect of gravity.)
 
It's now time to get ready for the big test!!
Sample test is next so have plenty of water (notice the motif) and hang on to your hat!