Question: Free fall problem, answer key at the vack and explain briefly
1. **Problem Statement:**
A body is dropped from rest and falls freely under gravity. Find the velocity of the body after falling for a time $t$ seconds.
2. **Formula Used:**
The velocity $v$ of a freely falling object after time $t$ is given by the equation:
$$v = gt$$
where $g$ is the acceleration due to gravity (approximately $9.8$ m/s$^2$).
3. **Explanation:**
- The object starts from rest, so initial velocity $u = 0$.
- Gravity accelerates the object downward at $g$ m/s$^2$.
- Velocity increases linearly with time under constant acceleration.
4. **Intermediate Work:**
Since $u=0$, the velocity after time $t$ is:
$$v = u + gt = 0 + gt = gt$$
5. **Final Answer:**
The velocity of the object after falling for $t$ seconds is:
$$\boxed{v = gt}$$
This means the velocity increases by $9.8$ m/s every second the object falls.