an object free falls for 5 seconds. how far does it fall from its initial position? -127.5 m 127.5 m -122.5 m

Explanation:

Step1: Identify the free - fall formula

The formula for the distance an object falls in free - fall is $d = v_0t+\frac{1}{2}gt^2$. Since the object starts from rest, $v_0 = 0$. The acceleration due to gravity $g=- 9.8\ m/s^2$ (negative because it acts in the downward direction).

Step2: Substitute the values

We have $t = 5\ s$, $v_0 = 0$, and $g=-9.8\ m/s^2$. Substituting into the formula $d = v_0t+\frac{1}{2}gt^2$, we get $d=0\times t+\frac{1}{2}\times(-9.8)\times5^2$.

Step3: Calculate the distance

First, calculate $5^2 = 25$. Then, $\frac{1}{2}\times(-9.8)\times25=- 122.5\ m$. The negative sign indicates the direction is downward.

Answer:

-122.5 m