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PastaTapestry

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**1. A blue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.9 m/s2. A green car arrives at the position of the stop-light 4 s after the light had turned green. What is the slowest constant speed which the green car can maintain and still catch up to the blue car?**

Answer in units of m/s

So, we're given that ##a = 0.9 m/(s^2)##, ##v_0 = 0##, and that displacement at t = 0 is 0 (all of this for the blue car, or ##C_B##)

For the green car(or ##C_G##), we're given that the car is holding a constant speed, so there must be no acceleration. If there's no acceleration, then the final and initial velocities must be equal for ##C_G##. Additionally, we're given that its displacement = 0 at t = 4 (since it started 4 seconds late).

Answer in units of m/s

So, we're given that ##a = 0.9 m/(s^2)##, ##v_0 = 0##, and that displacement at t = 0 is 0 (all of this for the blue car, or ##C_B##)

For the green car(or ##C_G##), we're given that the car is holding a constant speed, so there must be no acceleration. If there's no acceleration, then the final and initial velocities must be equal for ##C_G##. Additionally, we're given that its displacement = 0 at t = 4 (since it started 4 seconds late).

**2. We know that the velocity for ##C_B## is $$v=0.9t$$ We know that the displacement is equal to $$0.45t^2$$**

For ##C_G##, we know that ##v## is a constant c, that acceleration = 0, and that the displacement is represented by the function ##vt - 4v## (I believe).

For ##C_G##, we know that ##v## is a constant c, that acceleration = 0, and that the displacement is represented by the function ##vt - 4v## (I believe).

**3. I figured that we were looking for the minimum speed that ##C_G## would have to possess to cause the displacement of both ##C_G## and ##C_B## to be equal, because this would represent that ##C_G## had caught up to ##C_B##. However, I kept getting it down to things like $$0.45t^2 = vt - 4v$$ which you can't solve to my knowledge. So I tried a graphical method. I know that the displacement of ##C_B## is a parabola, and that the displacement of ##C_G## is a linear equation that passes through the point (4,0) [if we graph displacement as y and time as x). So we're looking for a tangent that passes through the point (4,0). However, we don't know the time or displacement this occurs at.**

Sorry if this is all too verbose and such, first time posting here so I apologize!

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