solution: part a.

First I will find the conditions of the race after 0.5 seconds when the friends starts to run.
After 0.5s: Jerry: tex2html_wrap_inline101 , tex2html_wrap_inline103

eqnarray14

Now we know how far ahead Jerry is when his friend starts running. Now that they are both moving, we can find relations for the positions of Jerry and his friend with respect to time.
At t=.5s: Jerry tex2html_wrap_inline105
At t=.5s: friend tex2html_wrap_inline107
tex2html_wrap_inline109
Set two equations for tex2html_wrap_inline111 equal to each other using data above.

eqnarray34

Use the quadratic Equation to solve for t:

eqnarray60

The negative root is discarded because we are only interested in what happens from t=0
tex2html_wrap117