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

At the instant you pass the Porsche, the x values (yours and the Porsche's) have to be equal. Using the general equation giving x as a function of time, write down two equations, one giving your position as a function of time and one giving the Porsche's position. The general equation is:

x = x_o + v_o t + ½ a t²

For you : x₁ = -15 + 11.11 t + 0

For the Porsche : x₂ = 0 + 0 + ½ (3) t² = 1.5 t²

Now what?

Set the equations equal, 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.

x₁ = x₂

-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. What do these two values mean?

To get the answer to question (a), plug t = 1.776 into either of your x expressions. Check your answer: both equations should give the same value.

For you, at t = 1.776 s, x₁ = 4.73 m.

For the Porsche, at t = 1.776 s, x₂ = 4.73 m.