To determine the change in the x-component of the velocity of an object, subtract the x-component of the initial velocity from the x-component of the final velocity.
True
False
Answer (2)
The change in the x-component of velocity is determined by subtracting the initial x-component from the final x-component, represented mathematically as Δ v x = v f x − v i x . Therefore, the statement is true. The process highlights a fundamental concept in physics regarding how we measure changes in motion.
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Define initial and final x-components of velocity: v i x and v f x .
Express the change in x-component of velocity as Δ v x = v f x − v i x .
Confirm that the change is calculated by subtracting the initial from the final.
Conclude that the statement is True .
Explanation
Problem Analysis The question asks whether the change in the x-component of velocity is found by subtracting the initial x-component of velocity from the final x-component of velocity.
Defining Change in Velocity The change in a quantity is generally defined as the final value minus the initial value. Let v i x be the initial x-component of the velocity and v f x be the final x-component of the velocity. The change in the x-component of velocity, denoted as Δ v x , is given by:
Calculating Change in Velocity Δ v x = v f x − v i x This means we subtract the initial x-component of the velocity from the final x-component of the velocity to find the change in the x-component of the velocity.
Conclusion The statement in the question aligns with the correct definition of the change in velocity. Therefore, the statement is true.
Examples
Understanding the change in velocity is crucial in many real-world scenarios. For example, when analyzing the motion of a car, the change in velocity (acceleration) helps determine how quickly the car speeds up or slows down. This concept is also vital in sports, such as calculating a baseball's change in velocity after being hit by a bat, which helps predict its trajectory and distance.
