Good Driver, Bad Decisions

Classical Mechanics Level 4

Devin is a troublemaker. While driving, Devin happens to see a police car stopped at a red light. Being the instigator that he is, Devin promptly pulls up his car even with the cop's, rolls down the window and throws a burrito in the cop's face. Immediately, Devin speeds off, knowing that he's in big trouble. The cop leaves the light at the same time, tailing closely behind.

Even though Devin loves to break the rules, he doesn't want to get in trouble for more than throwing a burrito. Because of this, Devin stops at every stop sign on the road, and slows down appropriately for each one. Ironically, the cop only cares about catching Devin and drives straight through every stop sign. Eventually, the policeman catches up with Devin, but not after traveling quite a ways down the road. How far did the policeman have to travel in order to catch up to Devin? Round your answer to the nearest thousandth of a meter.

Details and Assumptions

  • Devin and the cop start even with their front bumpers even at the stop light, and we are looking for the next point in time where the cop's front bumper is once again even with Devin's.

  • Both drivers start at \(0 \text{ m/s}\).

  • Devin drives at a constant rate of \(50\text{ m/s}\), but when a stop sign is approaching, he slows down at a rate of \(25 \text{ m/s}^2\) and reaches \(0 \text{ m/s}\) just as he reaches the stop sign, then immediately begins to reaccelerates at the same speed of \(25\text{m/s}^2\) until he reaches \(50\text{ m/s}\) again. Devin always accelerates and decelerates at \(25\text{m/s}^2\).

  • The policeman starts at \(0 \text{ m/s}\) at the light, then accelerates continuously at a rate of \(3 \text{ m/s}^2\) until he catches Devin.

  • There is a stop sign every \(300 \text{ m}\) down the road, and the first one is \(300 \text{ m}\) from the stop light.

  • Ignore friction and wind resistance.


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