A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 5.46 m/s^2.?

Question

A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 5.46 m/s^2. 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 1.172 before kathy. Stan moves with a constant acceleration of 3.95 m/s^2 and Kathy maintains an acceleration of 5.46 m/s^2

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 thtat instant. Answer in units of m/s.

Answer 1

Call stan's start time = 0.
The basic equation is based on the fact that, at the overtake point, velocities and accelerations averaged over time t are equal.
as = 3.95, ak = 5.46
a(average, stan) = as = a(average,kathy)
as = ak * (t-1.172)/t = ak * (1-1.172/t)
as/ak - 1 = -1.172/t
ans. 1. t = 1.172 / (1-as/ak)
ans. 2. sk = ak * (t-1.172)^2 / 2
ans. 3. vs = as*t
ans. 4. vk = ak*(t-1.172)