Question

A train is approaching a town at a constant speed of 12 m/s. The town is 1.0 km distant. After 30 seconds, the conductor applies the breaks. What acceleration is necessary to bring the train to rest exactly at the edge of town?

Answer 1

To solve this problem we will apply the linear motion kinematic equations. To determine the position in which the braking starts we will start from the definition of distance as a function of speed and time, that is

$x = x_0 - vt$

Here,

$x_0$ = Initial position

v = Velocity

t = time

Replacing we have that

$x = 1000-12*30$

$x = 640m$

Now the acceleration is given by the function,

$v_f^2=v_0^2 +ax$

Here,

$v_f$= Final velocity

$v_0$= Initial velocity

a = Acceleration

x = Displacement

Replacing we have that

$0 = 12^2+2a(640)$

$a = -0.1125m/s^2$

Therefore the acceleration necessary to bring the train to rest is $-0.1125m/s^2$