Calculating Time to Overtake in a Racing Scenario: A Physics Problem

[anti404]

hi, so here's a little background on why this may seem such a simple question to answer for others: I've never taken a physics course, or even a math course above the level of high-school precalculus. so here I am as a sophomore in college level intro. physics and have no idea how to solve any of these problems, as we are supposed to have a high-school physics background. alright, enough with that...


1. A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 4.96 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 1.11 s before Kathy. If Stan moves with a constant acceleration of 3.67 m/s2 and Kathy maintains an acceleration of 4.96 m/s2, find the time it takes Kathy to overtake Stan.
if I've read this correctly, we are given a1-4.96 m/s2, a2-3.67 m/s2, xo-0[for both racers], and vo-0[also for both racers]. we are looking for t1, the time at which Kathy's position is equivalent to Stan's position. again, if reading correctly, t1=t2-1.11s. I am using the (1) to reference Kathy and the (2) to reference Stan.



2. x = x_0 + v_0 t + (1/2) a t^2
I would assume, as we are trying to find time at a certain point[the position where both racers have met], given acceleration, that would be the most useful equation.


3. okay, honestly, I don't know what to do.
as we are relating two racers' relative positions and times, I'd assume we are trying to equate something like x= x_01 + v_01(t_01) + (1/2) a_1 (t_1)^2 to x=x_02 + v_02(t_02) + (1/2)a_2 (t_1)^2.
I attempted subtracting the equations to rid myself of variables, and then subbing t_1=t_2-1.11s into the equation, but that was not correct.

okay, well, that is all I know. I know it's not much, and if you are all unable to help, I understand, as that looks to be a jumbled mess.
well, I'll keep trying this myself, and hoping that someone is able to give me any advice, as I am really struggling to keep afloat here.

thanks all, Justin.

 

[rl.bhat]

Hi anti404, welcome to PF.
Your approach is correct.
Since Stan starts first, t_1 = t_2 + 1.11s.
Then x1 = x2. v_o = 0
So 1/2*a_1*t_1^2 = 1/2*a_2*t_2^2.
Substitute for t_1 and solve for t_2.

 

[anti404]

Hi anti404, welcome to PF.
Your approach is correct.
Since Stan starts first, t_1 = t_2 + 1.11s.
Then x1 = x2. v_o = 0
So 1/2*a_1*t_1^2 = 1/2*a_2*t_2^2.
Substitute for t_1 and solve for t_2.

hi thank you for the help (and the welcome =]).
so the final equation would probably look as such:
1/2(a_1)(t_2+1.11s)^2=1/2(a_2)(t_2)^2.
if I then carry out the squaring, I am left with:
1/2(a_1)(t_2^2+2.22t+1.2321)=1/2(a_2)(t_2)^2

it as at this point that I have been flustered for the past few days; I actually had the correct equation before posting this problem, but I seem to lack the basic mathematical understanding to complete it. not to be a bother, but could someone help me finish the solution?