4.5-4.6: Free Fall: How Fast & How Far

Elapsed Time

the time that has passed since the beginning of an event

However, accelerating objects aren't always falling. For an object that is constantly accelerating from rest.

v=at (velocity=acceleration x time)

For objects thrown straight up the speed decreases at the...

...same rate as it increases for objects falling (10 m/s²...) ...to the point where downward acceleration due to gravity overcomes upward velocity. After being zero for a moment, the object's velocity will begin to increase again (at 10m/s²), because the object is now falling back down.

The acceleration of an object in free fall is about...

10 meters per second squared (10m/s²) down (it is actually 9.8m/s², but we only need to use that when we want accuracy!)

So, 4.5 seconds after an object was dropped, its instantaneous speed would be...

45 m/s (v=gt, so v=10m/s² x 4.5s=45 m/s)

An object moving only under the influence of the gravitational force is said to be in...

free fall

How fast something moves is different from how far it moves.

Due to acceleration of gravity, falling objects move faster after each second elapsed. Because they move at a faster speed for each second-long period, they also fall larger distances each second-long period. (Between 0 and 1 seconds, the object falls 5 meters, but between 1 and 2 seconds, the object falls another 15 meters.)

Skydiving "free fall" is different from OUR Physics "free fall," because...

It is supposed to be ONLY the force of gravity for a Physics "free fall." With real-life free-falling objects and people, air resistance is another force involved. (air resistance is a form of friction, and we are assuming that we are in a frictionless environment)

The instantaneous speed (at a given moment) on an object falling from rest=

acceleration*elapsed time (at desired moment). This same idea can be expressed in equation form as v=gt... ...where v symbolizes both speed and velocity, g symbolizes the acceleration due to gravity, and t symbolizes elapsed time at the moment in question.

For free fall, it is customary to use the letter g to represent the...

acceleration, because the acceleration is due to gravity.

Thus, there must be an equation for us to easily calculate how far the object has fallen after a given period of time:

d (distance)=½gt²

and also how far... (horizontal distance equations)

d=½at²