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Repost: Maths/physics question by Arachnid2006-11-19 12:55:59
  OK, first the 4 basic kinematic equations by Talchas2006-09-25 15:57:31
    OK, the corrected answer for the second case: by Talchas 2006-09-25 16:07:06
t = ta = td 
t1=(vf - vtop)/ad
vtop=vi+at
d = vit+.5at2 + vtopt1+.5adt12
substitute and solve for t. I'd at least substitute + simplify for you, but I have to go. Here t1 is the time spent decelerating. You can use equation 3 of the basic equations to find the time spent when you can't reach the final speed (d=d, vi=vi,a=a or ad based on if vf is greater than or less than vi), and then equation 2 to find the actual final velocity.
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