Question

2 trains A and B are moving in same direction at same track with B ahead of A with speed u and train A with speed v (v>u). the driver of A sees B and starts decelerating with 'a'. What is the min distance to avoid collision

Answer 1

2 trains A and B are moving in same direction at same track with B ahead of A with speed u and train A with speed v (v>u). the driver of A sees B and starts decelerating with 'a'. What is the min distance to avoid collision?

Relative speed equals:

$$v _ {1 2} = (v - a t) - u$$

$d_0$ – initial distance, $t$ – time, $a$ – deceleration

min distance to avoid collision if $v_{12} = 0 \Rightarrow d = 0$

$$v _ {1 2} = 0 \quad \Rightarrow \quad t = \frac {v - u}{a}$$

Distance between trains at moment of time t:

$$d = d _ {0} - (v - u) t + \frac {a t ^ {2}}{2} = d _ {0} - \frac {(v - u) ^ {2}}{2 a}$$

min distance if $d = 0$:

$$d _ {0} = \frac {(v - u) ^ {2}}{2 a}$$

Answer: $d_0 = \frac{(v - u)^2}{2a}$