What is the velocity of an object that has been falling freely in a vacuum
for 4 seconds?
The Correct Answer and Explanation is :
To find the velocity of an object that has been falling freely in a vacuum for 4 seconds, we can use the equation of motion for free fall:
[
v = g \cdot t
]
where:
- ( v ) is the final velocity (in meters per second, m/s),
- ( g ) is the acceleration due to gravity (approximately ( 9.81 \, \text{m/s}^2 ) on the surface of the Earth),
- ( t ) is the time in seconds.
Given that the object has been falling for ( t = 4 ) seconds, we can substitute the values into the equation:
[
v = 9.81 \, \text{m/s}^2 \cdot 4 \, \text{s} = 39.24 \, \text{m/s}
]
Thus, the velocity of the object after falling freely for 4 seconds is approximately 39.24 m/s downward.
Explanation
When an object falls freely in a vacuum, it experiences constant acceleration due to gravity, which is approximately ( 9.81 \, \text{m/s}^2 ). A vacuum eliminates air resistance, allowing the object to accelerate without any opposing forces. This scenario contrasts with objects falling through the atmosphere, where air resistance can significantly affect their motion.
In the equation ( v = g \cdot t ), ( g ) is a constant that represents the acceleration of the object toward the Earth. Over time, the object’s velocity increases linearly, meaning that the longer it falls, the faster it goes, as it continuously gains speed from the gravitational pull.
For example, in this case, after 4 seconds, the object’s velocity reaches ( 39.24 \, \text{m/s} ). This straightforward calculation reflects how freely falling objects accelerate uniformly under the influence of gravity. It is important to note that this assumes no other forces are acting on the object, which is a reasonable approximation for a vacuum.