Chapter 4, Problem 19A

What is the appropriate equation for how fast an object freely falls from a position of rest? For how far that object falls?

To determine

The equation for velocity and displacement of a freely falling object.

Answer to Problem 19A

The equation for velocity of the object, v= g t.

Equation for the distance it falls, s = $\frac{\text{1}}{\text{2}}{\text{gt}}^{\text{2}}$

Explanation of Solution

Given:

Since object is falling freely, the only one force acting on it is the gravitational force in the downward direction. Therefore, the acceleration of the object is acceleration due to gravity

a = g

The object started from rest .Hence the initial velocity of the object u = 0 m/s

Let v is the velocity with which it falls and s is the displacement of object at a time t.

Formula used:

  $\begin{array}{l}\text{v = u+at}\\ \text{s = ut+}\frac{\text{1}}{\text{2}}{\text{gt}}^{\text{2}}\end{array}$

Calculation:

Substituting the given values, the velocity is

  $\begin{array}{l}\text{v = 0+gt}\\ \text{v = gt}\end{array}$

The distance travelled is,

  $\begin{array}{l}\text{s = 0+}\frac{\text{1}}{\text{2}}{\text{gt}}^{\text{2}}\\ \text{s=}\frac{\text{1}}{\text{2}}{\text{gt}}^{\text{2}}\end{array}$

Conclusion:

The object falls with a velocity v = g t

The object falls for distance s = $\frac{\text{1}}{\text{2}}{\text{gt}}^{\text{2}}$