A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 3.5m/s. Two seconds later the bicylicts hops on his bike and accelerates at 2.4m/s^2 until he catches his friend.
(a) How much time does it take until he catches his friend?
(b) How far has he traveled in this time?
(c) What is his speed when he catches up?

I sort of figured out part (a)but I'm not sure.. please explain!

You say you've "sorta figured out" part (a) - why don't you post your work and let us have a look at it?

Given the subject of the question, you should be able to find in your class notes two equations - one for distance travelled at a constant velocity, and one for total distance travelled at a constant acceleration. You need to set up an equation where these two distances are the same.

Once you've done that, the answers to parts (b) and (c) should be very easy to figure out.

hint: use v2=vo2+2a(x-xo), and v=vo+at