A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 4.16 m/s2. She decides to test the car by drag racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 0.58 s before Kathy. Stan moves with a constant acceleration of 2.88 m/s2 and Kathy maintains an accelera- tion of 4.16 m/s2.

Question

A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 4.16 m/s2. She decides to test the car by drag racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 0.58 s before Kathy. Stan moves with a constant acceleration of 2.88 m/s2 and Kathy maintains an accelera- tion of 4.16 m/s2.
Find the time it takes Kathy to overtake Stan. Answer in units of s
Find the distance she travels before she catches up with him. Answer in units of m
Find the speed of Stan’s car at the instant she overtakes him. Answer in units of m/s
Find Kathy’s speed at that instant. Answer in units of m/s

drwls · Answer

Let Kathy's distance from the starting point be x.
Let Stan's distance frm the starting point be y.
Let t = 0 be the instant that Stan starts. Kathy leaves 0.58 s later.

x = 2.08 (t-0.58)^2 (t > 0.58s)
y = 1.44 t^2

Set x = y and solve for t. Call that time t*

x(t*) is the distance travelled.
Stan's speed at that time is 2.88 t*
Kathy's speed at that time is 4.16(t*-0.58)