During a track event two runners, Mary, and Alice, round the last turn and head into the final stretch with Mary a distance d = 1.0 m in front of Alice. They are both running with the same speed of v0= 6.0 m/s. When the finish line is a distance L= 45.0 m away from Alice, Alice accelerates at aA = 0.5 m/s2 until she catches up to Mary. Alice then continues at a constant speed until she reaches the finish line.
How long (in s) did it take Alice to catch up with Mary?How far (in m) did Alice still have to run when she just caught up to Mary?How long (in s) did Alice take to reach the finish?

Question

During a track event two runners, Mary, and Alice, round the last turn and head into the final stretch with Mary a distance d = 1.0 m in front of Alice. They are both running with the same speed of v0= 6.0 m/s. When the finish line is a distance L= 45.0 m away from Alice, Alice accelerates at aA = 0.5 m/s2 until she catches up to Mary. Alice then continues at a constant speed until she reaches the finish line. 
How long (in s) did it take Alice to catch up with Mary?How far (in m) did Alice still have to run when she just caught up to Mary?How long (in s) did Alice take to reach the finish?

ganeshie8 · Answer

How long (in s) did it take Alice to catch up with Mary :

s = 1m
a = 0.5

$1 = 1/2 \times   0.5 \times t^2$

solve t