Safe Distance

A car and a truck are traveling in a row at the same speed of 90 km/h.

Suddenly, the car brakes to a complete stop, and then the truck comes to a complete stop to avoid hitting the car. How far apart (in meters) should the two vehicles be so that the truck avoids crashing into the car?

Details and Assumptions:

  • The car takes 40 m to brake to a complete stop, and the truck takes 100 m to brake to a complete stop.
  • The truck driver takes 1.2 seconds to react to the car braking.
  • The front of the truck will just barely touch the back of the car after the truck finishes stopping.

Bonus problem: How big should the safety distance be if the truck drives in front of the car? Assume that the car driver has the same reaction time of 1.2 s.

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