Understanding Deceleration in Trains: A Kinematic Analysis

When a train slows down from an initial speed to a complete stop over a certain distance, the deceleration can be calculated using the principles of kinematics. This article will delve into the process of determining the deceleration of a train that initially moves at 4 m/s and comes to a stop over a distance of 100 meters. By examining the relevant kinematic equations and following the step-by-step process, we can better understand the motion of the train.

Kinematic Equations and Their Use in Calculating Deceleration

The basic kinematic equations that govern motion are:

Here, (v) represents the final velocity, (u) represents the initial velocity, (a) is the acceleration (or deceleration, which is acceleration in the opposite direction), and (s) is the distance covered. In the case of the train, the final velocity (v) is 0 m/s, the initial velocity (u) is 4 m/s, and the distance (s) is 100 meters.

Applying the Kinematic Equation to Calculate Deceleration

Using the third kinematic equation (v^2 u^2 2as), we can calculate the deceleration of the train:

(0 4^2 2a cdot 100)

This simplifies to:

0 16 200a

Solving for (a), we get:

200a -16

(a -frac{16}{200} -0.08 , text{m/s}^2)

The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which means the train is decelerating. Thus, the deceleration of the train is 0.08 m/s2.

Conclusion

By applying the principles of kinematics, it is clear that deceleration can be calculated using the appropriate kinematic equations. In the case of the train that slows down from 4 m/s to a stop over a distance of 100 meters, the deceleration is found to be 0.08 m/s2. This understanding is valuable for engineers and physicists studying motion, as well as for anyone interested in the mechanics of train operations.

Keywords: kinematic equations, deceleration, acceleration