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.
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 $\displaystyle t_B$ be $\displaystyle x_B$. Then
$\displaystyle x_B = 30 t_B$ .... (1)
Data for Train A:
$\displaystyle x = (1500 + x_B)$ m
u = 80 m/s
v = 30 m/s
$\displaystyle t = t_B$ s
Use the usual formula $\displaystyle x = \left( \frac{u + v}{2} \right)t$:
$\displaystyle x_B + 1500 = \left( \frac{80 + 30}{2}\right) t \Rightarrow x_B = 55t - 1500$ .... (2)
Solve equations (1) and (2) simultaneously for $\displaystyle t_B$.
So for Train A you now have:
u = 80 m/s
v = 30 m/s
$\displaystyle t = t_B = ....$
a = ?
Use an appropriate formula to solve for a.