91Ó°ÊÓ

Understanding an inertial reference frame is crucial to grasp the principles of impulse and momentum. An inertial reference frame is essentially a viewpoint that either stays still or moves at a consistent speed without changing directions.
This means, in such a frame, objects do not experience any net external forces that could cause an acceleration. So, Newton's laws of motion, including the principle of impulse and momentum, hold true here.
In the given exercise, observer A is in a fixed inertial reference frame since no additional forces act on it other than the pre-defined parameters. This means that the calculations of force and motion dynamics are straightforward and can be calculated using standard physics formulas like F = ma. The consistency of physics in all inertial reference frames is what allows the calculation results, such as the block's final velocity, to be evaluated the same way by another observer in a different inertial frame, like observer B.

Force and motion are intimately linked through Newton’s second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration, expressed in the formula: \( F = ma \). In our exercise, this relationship helps us determine the acceleration of a block when a known force is applied.
With a block of 10 kg experiencing a horizontal force of 6 N, we can easily calculate the acceleration. By dividing the force by the mass, we get an acceleration of 0.6 m/s². This acceleration indicates how the velocity of the block will change over the course of time.
During a period of 4 seconds, the block's velocity increases due to this constant acceleration. Calculating the change in velocity, \( Δv = a \times t = 0.6 \times 4 = 2.4 \, \text{m/s} \), we see how motion is directly affected by force applied over time. If the initial velocity is known, we can then find the final velocity using \( v = v_0 + Δv \). Such straightforward calculations are possible thanks to the predictable relationship between force and motion.

Relative velocity is a concept that describes how the speed of an object changes as observed from different reference frames. This is particularly useful when observers in different frames measure the same physical process.
In the exercise, observer B moves with a constant velocity of 2 m/s relative to observer A. To find the initial speed of the block as seen by B, we subtract B's velocity from the block's velocity observed by A: \( 5 \, \text{m/s} - 2 \, \text{m/s} = 3 \, \text{m/s} \).
Despite the different initial readings, the block's acceleration due to the force remains unchanged because the force itself does not change between reference frames. Consequently, observer B observes the block accelerate by 2.4 m/s over 4 seconds, arriving at a final relative velocity of \( 5.4 \, \text{m/s} \).
Adding back B's velocity of 2 m/s gives a final velocity in line with observer A's calculations. Thus, both observers arrive at the same conclusion, demonstrating how relative velocity plays into understanding motion across different inertial frames.