What is the position function that represents motion under gravity?

The position function that represents motion under the influence of gravity, particularly in a context where the initial velocity and initial height are factored in, is given by the formula f(t) = -16t² + v₀t + h₀.

In this formula:

• The term -16t² accounts for the effect of gravity and is derived from the gravitational acceleration on Earth, which is approximately 32 feet per second squared. This negative sign indicates that gravity is pulling the object downward.

• The term v₀t represents the initial velocity multiplied by time, signifying how far the object travels due to its initial speed before the effects of gravity are fully felt.

• The term h₀ indicates the initial height from which the motion starts, reflecting the position of the object at time t = 0.

This formulation accurately captures the dynamics of an object thrown upwards or downwards under gravity, illustrating how the position changes over time due to both the initial conditions and gravitational pull. Therefore, this position function models the real-world behavior of projectile motion effectively.