- #1

Jenny Physics

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## Homework Statement

At a given time ##t=0##, a car 1 moving with constant velocity ##v_{1}## breaks with constant deceleration ##d##. Another car 2 at a distance ##L## behind car 1 and traveling with constant acceleration ##a_{2}## and velocity ##v_{2}## at ##t=0## brakes immediately as soon as it sees car 1 brake (zero reaction time). Both cars brake with the same deceleration ##d##. What is the critical (minimum) value of ##d## that will prevent the cars from colliding?

## Homework Equations

Kinematics for velocity, acceleration, position

## The Attempt at a Solution

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Car 1 has equation of motion ##x_{1}=L+v_{1}t-\frac{1}{2}dt^{2}##.

Car 2 has equation of motion ##x_{2}=v_{2}t-\frac{1}{2}dt^{2}##

(I don't think I need to use ##a_{2}##?)

The cars will collide if ##x_{1}=x_{2}##. But that doesn't give any constraint on ##d##.