91影视

Free fall is represented as the occurrence of a specific object being released from a height toward the ground.

For example, meteors falling toward the ground, movement of spacecraft in continuous orbit, and many others.

The relation from the equation of motion is given by.

$S=ut+\frac{1}{2}g{t}^2$

Here, u is the initial speed whose value is zero, g is the gravitational acceleration, S is the distance traveled, and t is the time.

On plugging the values in the above relation, you get.

role="math" localid="1643005824541" $\begin{array}{c}S\left(t\right)=0脳t+\frac{1}{2}g{t}^2\\ S\left(t\right)=\frac{1}{2}g{t}^2鈥�\left(i\right)\end{array}$

Substitute $t+1$for $t$in equation (i).

$S\left(t+1\right)=\frac{1}{2}g{\left(t+1\right)}^2$

The relation to show the distance traveled during each successive second is given by.

role="math" localid="1643005934633" $\begin{array}{l}S\left(t+1\right)-S\left(t\right)=\left[\frac{1}{2}g{\left(t+1\right)}^2-\frac{1}{2}g{t}^2\right]\\ S\left(t+1\right)-S\left(t\right)=\frac{g}{2}\left[2t+1\right]鈥�\left(ii\right)\end{array}$

At time $t=0$, the value of time $2t+1$is 1.

At time $t=1$, the value of time $2t+1$is 3.

At time $t=2$, the value of time $2t+1$is 5.

Thus, it is shown that the distance traveled during each successive second increases in the ratio of successive odd integers.