Can you help me with this problem??

Question

At the half way mark of a 200 meter race the lead runner is running at a uniform speed of 10.3 m/s. The contestant in the second position is running at a speed of 10.1 m/s is 2 meter behind the leader. If the athlete in the second position wants to win the race what should be his minimum value of uniform acceleration (ms^-2) required from this point?

Answer 1

Let a = acceleration of runner 2 = constant

Let v1 = speed of runner 1 = 10.3 m/s

Let v2 = speed of runner 2

Let v2o = speed of runner 2 at halfway point

Let x1o= 0 = position of runner 1 at time =0

Let x2o = -2 = position of runner 2 at time =0

Since v1 is constant x1= tv1

Since runner 2 is accelerating uniformly, v2=at+v2o and x2=x2o+.5at2+v2ot+x2o

Let T = time at end of race and x2 > x1 for runner 2 to win

Set x1=100 to find t = T= 100/10.3

Set x2=100 and solve for a