(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

At the instant the traffic light turns greeen, Stan Speedy starts from rest and accelerates at "a". At the same instant Kathy Kool starts from rest "d" behind Stan and accelerates at "5/4a" (not sure, but I think this is meant to be (5/4)a or 5a/4, my attempts with "5/4a" gave me strange answers).

Given [a, d], determine:

a.How far beyond the starting point do they meet again.

b.The time before they meet again.

c.How fast is each moving when they meet again.

2. Relevant equations

displacement & time:

x=x0+v0t+(1/2)at2

velocity & time:

v=v0+at

velocity & displacement:

v2=v20+2aΔx

3. The attempt at a solution

I've attached an image that shows a diagram I drew to help me solve the problem. Whether it be correct or not, that I do not know.

The only approach I could think of was to first set x=x0+v0t+(1/2) for each car equal to each other, that is, when each car would reach x_{1}

Since each car is starting from rest, I believe that v_{0}=0

Stan's Car:

x_{1}=(0)t+[itex]\frac{1}{2}[/itex]at^{2}

x_{1}=[itex]\frac{1}{2}[/itex]at^{2}

Kathy's Car:

x_{1}=(0)t+[itex]\frac{1}{2}[/itex][itex]\frac{5a}{4}[/itex]t^{2}

x_{1}=[itex]\frac{5a}{8}[/itex]t^{2}

Stan's x_{1}= Kathy's x_{1}

[itex]\frac{1}{2}[/itex]at^{2}=[itex]\frac{5a}{8}[/itex]t^{2}

My reasoning for this was to then solve for t so that I would then know at what time that these two cars would be at the same point, and then I could use t to help me calculate the other unknowns, but whenever I try to solve for t, I get 0, which doesn't make much sense to me.

I think my problem is that I'm not accounting for the starting distance between Kathy's and Stan's car at the beginning of the problem.

I've been racking my head over this for hours

(physics and math aren't necessarily by best subjects )

A great many thanks to any who can point me in the right direction on this.

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# Homework Help: Constant Acceleration Problem - Two bodies with different accelerations

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