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Chapter 1: Problem 17

How does the velocity of a freely falling body change with time? How does the distance it has fallen change? How about the acceleration?

Short Answer

Expert verified
Answer: During free fall, the velocity of the object increases linearly with time, the distance fallen increases nonlinearly (quadratically) with time, and the acceleration remains constant and equal to the acceleration due to gravity (approximately 9.81 m/s虏).

Step by step solution

01

1. Review the kinematic equations for constant acceleration

The two fundamental kinematic equations for constant acceleration are as follows:\newline 1) \(v = u + at\) (where \(v\) is the final velocity, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is time)\newline 2) \(s = ut + \frac{1}{2}at^2\) (where \(s\) is the displacement, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is time)
02

2. Apply the equations to free fall

In the case of free fall, the only force acting on a body is gravity. Let's assume that the acceleration due to gravity, \(g\), is approximately 9.81 m/s虏 downward. Since the body is falling freely, we'll consider downward direction as positive. So, the acceleration, \(a\), will be equal to \(g\). Our revised kinematic equations for free fall are:\newline 1) \(v = u + gt\)\newline 2) \(s = ut + \frac{1}{2}gt^2\)
03

3. Analyze the change in velocity with time

Using the first revised kinematic equation, we can find how the velocity changes with time in free fall:\newline \(v = u + gt\)\newline Since the acceleration due to gravity \(g\) is constant, the velocity will increase linearly with time during free fall.
04

4. Analyze the change in distance fallen with time

We can use the second revised kinematic equation to find how the distance fallen changes with time in free fall:\newline \(s = ut + \frac{1}{2}gt^2\)\newline Because the acceleration due to gravity \(g\) is constant, the distance fallen is a quadratic function of time, meaning that it will increase nonlinearly.
05

5. Analyze the change in acceleration with time

The acceleration in the case of free fall is constant and equal to the acceleration due to gravity, \(g\). This means that there will be no change in acceleration during free fall, and its value remains constant at 9.81 m/s虏 (assuming Earth's gravitational pull). In summary, during free fall, the velocity of the object increases linearly with time, the distance fallen increases nonlinearly (quadratically) with time, and the acceleration remains constant and equal to the acceleration due to gravity.

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