Question

1. a stone that starts at rest is in free fall for 8.0 s.

a. calculate the stone’s velocity after 8.0 s. m/s
b. what is the stone’s displacement during this time?

Explanation:

Step1: Identify the formula for velocity in free - fall

The formula for the velocity $v$ of an object in free - fall is $v = v_0+gt$, where $v_0$ is the initial velocity, $g$ is the acceleration due to gravity ($g = 9.8\ m/s^2$), and $t$ is the time. Since the stone starts at rest, $v_0 = 0\ m/s$.
$v=v_0 + gt$

Step2: Calculate the velocity

Substitute $v_0 = 0\ m/s$, $g = 9.8\ m/s^2$, and $t = 8.0\ s$ into the formula.
$v=0+9.8\times8.0$
$v = 78.4\ m/s$

Step3: Identify the formula for displacement in free - fall

The formula for the displacement $d$ of an object in free - fall is $d=v_0t+\frac{1}{2}gt^2$. Since $v_0 = 0\ m/s$, the formula simplifies to $d=\frac{1}{2}gt^2$.
$d=\frac{1}{2}gt^2$

Step4: Calculate the displacement

Substitute $g = 9.8\ m/s^2$ and $t = 8.0\ s$ into the formula.
$d=\frac{1}{2}\times9.8\times8.0^2$
$d = 313.6\ m$

Answer:

a. $78.4\ m/s$
b. $313.6\ m$