A projectile is fired directly upward with a velocity of 144ft/sec.
Its height in feet above ground after s(t)=144t-16t^2. What is the
velocity and acceleration after t sec? after 3 Sec? What is the max?
When does it strike the ground?

Thanks for the help!!

You simply have to take the derivitave of your function to get the
formula for velocity. Height = 144t - 16t^2 so, velocity = 144 - 32t.
the velocity at t or V(t)= 144-32t, the velocity at 3 seconds, V(3) =
144 - 32(3) = 48. To find out when it hits the ground, you want height
to equal 0. So 0 = 144t - 16t^2
16t^2 = 144t 16t = 144 t = 144/16 t = 9. So it would hit the ground after 9 seconds.