For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics.
David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?
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1
Identify the given values: David's constant speed is 30 m/s, and Tina starts from rest and accelerates at 2.0 m/s².
Set up the equations of motion for both David and Tina. For David, since his speed is constant, his position at any time t can be given by x_D = 30t. For Tina, starting from rest and accelerating, her position can be described by x_T = 0.5 * a * t², where a is her acceleration.
Set the equations equal to each other to find the time when Tina catches up to David. This means solving 30t = 0.5 * 2.0 * t² for t.
Once the time t is found, substitute it back into either David's or Tina's position equation to find the distance at which Tina passes David.
Check the units and make sure they are consistent throughout the calculations to ensure the accuracy of the result.