Kinematic Motion: How Far and How Fast Does Tina Drive Before Passing David?

[optoracko]

Homework Statement

David is driving a steady 30.0 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s^2 at the instant when David passes.
a. How far does Tina drive before passing David?
b. What is her speed as she passes him?

Velocity init. for Tina = 0 m/s
Velocity final for Tina = 30.0 m/s
Tina's acceleration = 2.0 m/s^2

Homework Equations

V₂² = V₁² + 2a(change in time)

The Attempt at a Solution

I've plugged these values into this equation to get 225m. I'm not sure what I'm doing it correct, though. It does not sound correct to me. My other idea was to graph their velocity at the moment David passes Tina and figure the answers out graphically. Is there a way to do this algebraically?

 

[andytuki]

Lets set some coordinates. Position of Tina is zero. She will travel X distance when she catches up with David. David travels to position X too when Tina reaches him. Two equations that have the same distances and the same time (time it takes to reach position X).

Tina (Using our coord. the intial position is zero, acceleration is known, Vi is unknown.)
x = xi + Vi*t + (1/2)*a*t^2

David (using our coord. the initial position is zero, Vi is known, and has no acceleration.)
x = xi + Vi*t + (1/2)*a*t^2

The distances are equal so set the two equations equal to each other and solve for Time, then use your other equation to solve for final velocity. Plug back in your variables to solve for the distances.