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 initial - velocity and acceleration

The stone starts at rest, so the initial velocity $v_0 = 0\ m/s$. The acceleration due to gravity $g=9.8\ m/s^{2}$ and the time $t = 8.0\ s$. The formula for velocity in free - fall is $v=v_0+gt$.

Step2: Calculate the velocity

Substitute the values into the formula: $v = 0+9.8\times8.0$.
$v=78.4\ m/s$

Step3: Identify the formula for displacement

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

Step4: Calculate the displacement

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

Answer:

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