Question

A steam train moving with a speed of v = 60 km/h is brought to rest by first shutting off the steam when the train runs against a resistance equal to 1/100 of its weight, and later by applying the brakes when the train runs against a force 1/8 of the weight of the train. If the steam is shut off when the train is a distance d = 0.33 km from a station, find the distance from the station that the brakes must be applied in order that the train may be brought to rest in the station.

A) 2.7 km
B) 3.0 km
C) 2.4 km
D) 3.3 km

Answer 1

To find the distance from the station that the brakes must be applied in order to bring the train to rest, we need to consider the forces involved. First, when the steam is shut off, the train runs against a resistance equal to 1/100 of its weight. This results in a deceleration. We can calculate the deceleration using the formula a = F/m. Next, we can calculate the distance travelled when the brakes are applied. We can use the equation d = vi*t + (1/2)at^2.

Step-by-step explanation:

To find the distance from the station that the brakes must be applied in order to bring the train to rest, we need to consider the forces involved. First, when the steam is shut off, the train runs against a resistance equal to 1/100 of its weight. This results in a deceleration. We can calculate the deceleration using the formula:

a = F/m

Where a is the deceleration, F is the force, and m is the mass of the train.

Next, we can calculate the distance travelled when the brakes are applied. We can use the equation:

d = vit + (1/2)at2

Where d is the distance travelled, vi is the initial velocity, t is the time taken to come to rest, and a is the deceleration.

Substituting the given values into the equations, we can find the distance from the station that the brakes must be applied. The correct option is B) 3.0 km.