Show that the equation for a stopping distance for a car x_stop = v_0 t_r - v_0

Question

Show that the equation for a stopping distance for a car x_stop = v_0 t_r - v_0 ^2 / 2a here v_0 is the initial speed of the car and t_r is the reaction time and a is the negative acceleration for stopping. What is generally your reaction time? In designing traffic lights, it is necessary to have the yellow light long enough so that a driver can completely stop before the signal or pass safely the intersection. So if the driver is less than x stop from the intersection, then the light must remain long enough for him to cover that distance + the intersection distance X_i (say). Show that yellow light must remain on for t = t_r - V_0 / (2a) + X_i / v_0, here t_r is the reaction time of the driver.

Explanation / Answer

general reaction time 5-10 s

yellow light has to remain on for 1. reaction time 2. time taken to cover stopping distance 3. time taken to cover intersection distance

= tr - vo/(2a) + xi/vo

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