# Math Help - rate of train decelerating to avoid a crash

1. ## rate of train decelerating to avoid a crash

train A which travels 80m/s is 1,500m behind trainB which is traveling at 30m/s in the same direction on the same track.at what rate must train Adecelerate to avoid a crash?

if anyone could help,
thanks Ronan.

2. Originally Posted by ronan116
train A which travels 80m/s is 1,500m behind trainB which is traveling at 30m/s in the same direction on the same track.at what rate must train Adecelerate to avoid a crash?

if anyone could help,
thanks Ronan.
The minimum constant deceleration will have train A travelling at 30 m/s when it is at the same position as train B.

Let the distance travelled by train B at time $t_B$ be $x_B$. Then

$x_B = 30 t_B$ .... (1)

Data for Train A:

$x = (1500 + x_B)$ m
u = 80 m/s
v = 30 m/s
$t = t_B$ s

Use the usual formula $x = \left( \frac{u + v}{2} \right)t$:

$x_B + 1500 = \left( \frac{80 + 30}{2}\right) t \Rightarrow x_B = 55t - 1500$ .... (2)

Solve equations (1) and (2) simultaneously for $t_B$.

So for Train A you now have:

u = 80 m/s
v = 30 m/s
$t = t_B = ....$
a = ?

Use an appropriate formula to solve for a.