(a) How far from the stop line do you pass the Porsche?

At the instant you pass the Porsche, the x values of your car and the Porsche must be equal. Let's write the general equations for x(t):

General equation: x = xo + vo t + ½ a t2

For your car : xyou = -15 + 11.11 t + 0

For the Porsche : xPorsche = 0 + 0 +½ (3) t2 = 1.5 t2

Now what?

Set xyou = xPorsche, and solve for the time(s) when the two cars are at the same position. Then plug the time back into the x equation(s) to find the position.

xyou = xPorsche   leads to:     -15 + 11.11 t = 1.5 t2

Bringing everything to one side gives:   1.5 t2 - 11.11 t + 15 = 0

Solve using the quadratic formula:      

where a = 1.5, b = -11.11, and c = 15

This gives two values for t, t = 1.776 s and t = 5.631 s.

To answer question (a), plug t = 1.776 into either of your x expressions. Both equations must give the same value. This serves as a useful check!

For you, when t = 1.776 s, xyou = 4.73 m.

For the Porsche, when t = 1.776 s, xPorsche = 4.73 m.