A resultant force F accelerates a car of mass m along a straight horizontal road fromrest to a speed v in time t, giving it momentum p. Which pair of relationships for thissituation is correct?(A) pt = mv and F = pt (B) p = mv and F = pt (C) p = mv and Ft = p (D) p = mvtand Ft = v
Question
A resultant force F accelerates a car of mass m along a straight horizontal road fromrest to a speed v in time t, giving it momentum p. Which pair of relationships for thissituation is correct?(A) pt = mv and F = pt (B) p = mv and F = pt (C) p = mv and Ft = p (D) p = mvtand Ft = v
Solution
The correct pair of relationships for this situation is (C) p = mv and Ft = p.
Here's why:
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Momentum (p) is defined as the product of mass (m) and velocity (v). So, p = mv is the correct relationship for momentum.
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Force (F) is the rate of change of momentum. In other words, it's the change in momentum (p) over time (t). So, the total change in momentum over time t is Ft. Since the car starts from rest, its initial momentum is 0, and its final momentum after time t is p. Therefore, Ft = p is the correct relationship for force.
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