Force, Change in Momentum, and Time Relationship

Introduction:
The relationship between force (F), change in momentum (p), and time (t) can be described using Newton's second law of motion. Newton's second law states that the force acting on an object is equal to the rate of change of its momentum. Mathematically, it can be represented as F = dp/dt, where F is the force, p is the momentum, and t is the time.

Explanation:
To determine the relationship between F, p, and t, we need to rearrange the equation F = dp/dt. By multiplying both sides of the equation by dt, we can isolate dp:

F * dt = dp

This equation shows that the change in momentum (dp) is equal to the force (F) multiplied by the change in time (dt).

Now, let's consider the units of the variables involved. Force is measured in Newtons (N), momentum is measured in kilogram meters per second (kg·m/s), and time is measured in seconds (s). Based on these units, we can determine the correct relationship between F, p, and t.

Analysis of Answer Options:
a) F = pt: This option is incorrect because it suggests that force (F) is equal to the product of momentum (p) and time (t). However, since momentum is measured in kg·m/s and time is measured in seconds, the units on the right side of the equation would be kg·m/s^2, which are the units for acceleration, not force.

b) F = p/t: This option is the correct answer. Dividing both sides of the equation F * dt = dp by dt gives us F = dp/dt, which is Newton's second law. This equation states that force (F) is equal to the change in momentum (dp) divided by the change in time (dt), which is consistent with Newton's second law.

c) Ft^2 = pd: This option is incorrect because it suggests that the product of force (F) and the square of time (t^2) is equal to the product of momentum (p) and displacement (d). This equation does not correctly represent the relationship between force, momentum, and time.

d) p = F^2t: This option is incorrect because it suggests that momentum (p) is equal to the square of force (F) multiplied by time (t). This equation does not correctly represent the relationship between force, momentum, and time.

Conclusion:
The correct relationship between force (F), change in momentum (p), and time (t) is given by option B: F = p/t. This equation is derived from Newton's second law of motion, which states that force is equal to the rate of change of momentum. The equation represents a fundamental relationship in physics and is widely used to understand the effects of forces on objects in motion.