Freight trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of 0.550 m/s2 , how long will it take to come to a stop from this velocity? (c) How far will it travel in each case?

Part (a)

Step 1 of 9:

The acceleration of a freight train is provided and since these kinds of trains are used for transporting goods, they have very fewer accelerations and decelerations. We are going to find the final velocity of the train if the train is starting with a particular initial velocity.

Acceleration produced

Time taken to reach the final velocity

The initial velocity

Step 2 of 9:

To find the final velocity of the train, from equation of motion

Inserting all numerical quantities to get final velocity v

The final velocity of the train is 28.00 ms-1

Part (b)

Step 3 of 9:

The train is moving with the velocity 28.00 ms-1 and the brake is applied on the train. Now the train starts decelerating and stops eventually. The deceleration rate is given by 0.550 m/s2. Deceleration is nothing but the negative acceleration. We are going to find the time taken by the train to stop completely. the Therefore

The acceleration produced

The final velocity of the train

The initial velocity of the train

Step 4 of 9:

From equation (1)

Substituting the values

The time taken by the train to stop completely is 50.91 s

Part (c)

Step 5 of 9:

Since the train moving with certain velocities, we can able to calculate the distance traveled by train in each case. The initial and final velocities are known with time duration. Taking average velocity of the journey will be useful in this calculation

In the first case:

Time taken to reach the final velocity

The initial velocity

The final velocity