Physics C question?

Question

Kathy Kool buys a sports car that can accelerate at the rate of 4.70 m/s2. She decides to test the car by dragging with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 1.00 s before Kathy. Stan moves with a constant acceleration of 3.80 m/s2, and Kathy maintains an acceleration of 4.70 m/s2.
(a) Find the time it takes Kathy to overtake Stan.
s
(b) Find the distance she travels before she catches him.
m
(c) Find the speeds of both cars at the instant she overtakes him.
Kathy
m/s
Stan
m/s

Answer 1

S1=S2
t1=t2-1
S=0.5at^2

S1=0.5a1 t1^2
S2=0.5a2 t2^2 since t1=t2-1
S2=0.5a2 (t1+1)^2
S1=S2
0.5a1 t1^2=0.5a2 (t1+1)^2
a1 t1^2=a2 (t1+1)^2
(a) solve for t1, add 1 sec and you have Kathy's speed
(b) Now compute S2=0.5a2 t2^2
(c) V1=a1t1 and V2= a2t2