Which of the following statements is correct?

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BlackTom AI · Accepted Answer

To begin, let's break down what each statement claims about force, momentum, and impulse.
Option 1: 'Force equals the change of momentum.' This is imprecise because the exact relation is that force equals the rate of change of momentum, not the finite change itself. The change in momentum over a time interval equals impulse; if you consider a finite interval, the average force equals the change in momentum divided by the time interval, but the instantaneous force is tied to the rate of change, not simply the total change.
Option 2: 'Momentum is a scalar quantity.' In fact, momentum is a vector quantity: it has both magnitude and direction equal to mass times velocity. Treating momentum as scalar ignores direction, which leads to incorrect conclusions in dynamics problems, especially when directions matter.
Option 3: 'Force equals rate of change of momentum.' This aligns with the fundamental form of Newton's second law in its differential version: F = dp/dt, where p is momentum. It accurately describes how force is connected to how quickly momentum changes with time.
Option 4: 'Impulse of a force is the differentiation of the force with respect to time.' This statement confuses impulse with the time derivative of force. Impulse is defined as the integral of force over time, J = ∫F dt, and it equals the change in momentum, not the derivative of force itself.
In summary, the first option misstates the relationship between force and momentum over time, the second mischaracterizes momentum, the third correctly states the fundamental relation, and the fourth confuses impulse with the time derivative of force. The nuanced distinctions between instantaneous rate of change, finite change over an interval, and impulse are crucial for accurate physics reasoning.

INU1127 (24/25) Momentum and Impulse - Quiz 2

Which of the following statements is correct?

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