91Ó°ÊÓ

Newton's Second Law is a fundamental principle in physics that describes how the motion of an object is affected by forces. It states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
This can be expressed with the formula:

• \( F = ma \)

In this context, a suitcase on a berth in a train experiences a force due to the train's deceleration. As the train slows down, the negative acceleration, or deceleration, occurs. The negative sign indicates the direction of acceleration is opposite to the initial movement of the train.
Newton's Second Law helps in calculating the forces needed to keep the suitcase stationary relative to the train. The law indicates that if a sufficient opposing force is not applied (like friction), the suitcase will start to move.

Deceleration is simply the negative acceleration. It happens when an object reduces its speed. There can be different causes for deceleration, such as applying brakes to a moving object.
To calculate deceleration, the formula used is:

• \( a = \frac{v_f - v_i}{t} \)

where:

• \( v_i \) is the initial velocity
• \( v_f \) is the final velocity
• \( t \) is the time taken for the change in velocity

In the train situation, the initial speed is 40 m/s, and the final speed is 20 m/s over a period of 5 seconds. By substituting these into our formula, we find that the deceleration (or the rate of slowing down) is \(-4 \, \text{m/s}^2\).
This value helps in understanding how quickly the object is stopping and ensures we can calculate the necessary conditions to maintain equilibrium, like through friction.

The coefficient of friction, often denoted by \( \mu \), is a measure of how much frictional force exists between two surfaces. It plays a crucial role in determining whether an object maintains its position when forces are applied.
This dimensionless number ranges between 0 and 1 (though it can be higher for very sticky surfaces). In physics problems, the coefficient of friction helps decide whether an object will slide over a surface or remain stationary.
For the train exercise, the coefficient of friction tells us whether the suitcase will stay in place during the train's deceleration. We derive it using the equation:

• \( \mu = \frac{|a|}{g} \)

With \( |a| = 4 \, \text{m/s}^2 \) and \( g = 9.8 \, \text{m/s}^2 \), the calculated \( \mu \) is approximately 0.41. Thus, comparing it to the choices provided, only a coefficient higher than 0.41 will ensure the suitcase does not slide, making 0.5 the safest choice.