Question

A train of mass 55,200 kg is traveling along a straight level track at 26.8 m/s. Suddenly the engineer sees a truck stalled on the tracks 184 m ahead. If the maximum possible braking acceleration has a magnitude of 1.52 m/s^2, can the train be stopped in time?

A) yes
B) no

Answer 1

Using the kinematic equation, it is calculated that the train requires 236.84 meters to stop. However, since there are only 184 meters available, the train cannot be stopped in time to avoid hitting the truck on the tracks.

Step-by-step explanation:

To determine whether the train can be stopped in time, we can use the equation of motion s = v2 / (2a), where s is the stopping distance, v is the initial velocity, and a is the deceleration. Substituting the given values for the train's initial velocity (26.8 m/s) and maximum deceleration (1.52 m/s2), we get s = (26.8 m/s)2 / (2 * 1.52 m/s2) = 236.84 m. Since the train needs to stop in less than 184 m and the calculated stopping distance is greater than that, the train cannot be stopped in time.