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When an object is in free fall, like a flowerpot falling from a window, it is moving under the influence of gravity alone. On Earth, this gravitational force accelerates objects downwards at approximately 9.81 m/s². This means every second, its velocity increases by 9.81 m/s.
This concept of motion under gravity is crucial in understanding how objects behave when they fall. We assume there is no air resistance, meaning that each falling object's motion solely results from gravity. This assumption simplifies calculations and lets us use specific kinematic equations to predict the object's behavior.
It's essential to know that motion under gravity affects all objects equally if no other forces are acting upon them, meaning they all accelerate similarly regardless of their masses.

Kinematic equations describe the motion of objects. They are particularly helpful for understanding motion under constant acceleration, such as motion under gravity. These equations allow us to calculate unknown variables like distance, final velocity, and time, using known variables.
Three primary kinematic equations are most commonly used:

• \( v = u + at \)
• \( s = ut + \frac{1}{2}at^2 \)
• \( v^2 = u^2 + 2as \)

- \( v \) is the final velocity.- \( u \) is the initial velocity.- \( a \) is the acceleration.- \( t \) is the time.- \( s \) is the displacement or distance.
In the flowerpot example, these equations help us find how far it fell before passing the window by recognizing that the pot accelerated uniformly downwards.

To solve problems with motion under gravity, calculating the initial velocity can be necessary, as it was in the flowerpot example. Even if we don't initially know this value, it can be derived using kinematic equations.
By rearranging the kinematic equation \( s = ut + \frac{1}{2}at^2 \), where \( s \) is the distance travelled, we can solve for the initial velocity \( u \). Given enough information about the other quantities involved, manipulating these equations allows us to isolate and find the unknown \( u \).
In our example, the initial velocity was determined through analyzing how fast the flowerpot was moving at the top of the window. Once we have this value, it gives us enough information to backtrack and compute the distance it fell from the windowsill to the window's top.