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## AP®︎/College Physics 1

### Unit 1: Lesson 7

Objects in freefall

# Freefall review

Review the key concepts and skills for acceleration due to gravity, including analyzing motion of objects in freefall.

## Key terms

TermMeaning
Acceleration due to gravityIn the absence of air resistance, all objects fall with constant acceleration start text, g, end text toward the surface of the Earth. On the surface of Earth, defined as g, equals, 9, point, 8, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction.

## Analyzing motion for objects in freefall

Freefall is a special case of motion with constant acceleration, because acceleration due to gravity is always constant and downward. This is true even when an object is thrown upward or has zero velocity.
For example, when a ball is thrown up in the air, the ball's velocity is initially upward. Since gravity pulls the object toward the earth with a constant acceleration g, the magnitude of velocity decreases as the ball approaches maximum height.
Figure 1. Direction of velocity and acceleration for a ball thrown up in the air. Acceleration from gravity is always constant and downward, but the direction and magnitude of velocity change.
At the highest point in its trajectory, the ball has zero velocity, and the magnitude of velocity increases again as the ball falls back toward the earth (see figure 1).

## Common mistakes and misconceptions

People mistakenly think the final velocity for a falling object is zero because objects stop once they hit the ground. In physics problems, the final velocity is the speed just before touching the ground. Once it touches the ground, the object is no longer in freefall.

For deeper explanations of freefall, see our videos plotting projectile motion and impact velocity from a given height.
To check your understanding and work toward mastering these concepts, check out our exercises freefall concepts and graphs and using kinematic formulas to solve freefall problems.

## Want to join the conversation?

• An astronaut holds a rock at 100m above the surface of Planet X. The rock is thrown upward with a speed of 15m/s. The rock reaches the ground 10s after it is thrown. The atmosphere of Planet X has a negligible effect on the rock when it is in free fall.
Based on my calculations, I found that the acceleration due to gravity of the rock when it is on Planet X is -1.5m/s^2. How does the speed of the rock when it reaches the ground vd compare to the speed of the rock when it is thrown upward vu?
____vd > vu____vd = vu____vd < vu
• *note: the _ symbol refers to a subscript. So, v_f refers to the final velocity.

Sorry, but I believe the acceleration is -5m/(s^2).
x_f = x_i + v_i(t) + 0.5at^2
0m = 100m + (15m/s)(10s) + 0.5a(10s)^2
-100m = 150m + 50s^2a
-250m = 50(s^2)a
a = -5m/s^2

Now to the answer. The velocity as the rock reaches the ground will be greater than the initial velocity. Just try substituting values to test this out.

v_f = v_i + at
v_f = 15m/s - 5m/s^2(10s)
v_f = 15m/s - 50m/s
v_f = -35m/s
speed_f = |v_f|
speed_f = |-35m/s|
speed_f = 35m/s
Therefore, speed_f > speed_i.
• What is the difference between Terminal Velocity and Constant Speed?
• CONSTANT VELOCITY =>If you say that velocity is constant, is just a way to say that the velocity does not change with time...;)

TERMINAL VELOCITY => When an object which is falling under the influence of gravity which increases with velocity, it will ultimately reach a maximum velocity where the drag force equals the driving force. This final, constant velocity of motion is called a "terminal velocity", a terminology made popular by skydivers..:)

HOPE U GET IT ;)
• How do you calculate air resistance?
• Does anyone here like tacos?
• How do you determine whether the acceleration (due to gravity) is positive or negative.
• If you dont mind me answering, we know that acceleration due to gravity is positive or negative when the question we are doing tells us that either upwards is positive or negative. For example if they tell us that upwards is positive that means downwards is negative and acceleration due to gravity is always downwards (in this context of 1d motion ofcourse) So the positive or negative sign is determined by the convention of the question.

I hope that helped. anyone in the forum please correct me if i am wrong.
thx
• Hey, what is the connection between gravity and air resistance?
• A ball is thrown straight upwards with an initial velocity of 10 meters per second. Acceleration due to gravity is 9.81 meters per second squared downward. Does the ball come to rest in mid-air? If so, why? How many seconds after release does the ball come to rest? How high is the ball above the initial position when it comes to rest?