Question

How can Newon's "Suvat" equations be adjusted for the fact that acceleration of an object falling from a great height is not constant and that a terminal velocity is reached?

Answer 1

When an object falls from a great height, the acceleration due to gravity is not constant throughout its entire motion. Initially, the object experiences an acceleration close to the value of gravitational acceleration (9.8 m/s² near the surface of the Earth), but as it gains speed, the effects of air resistance become significant. Eventually, the object reaches a terminal velocity where the upward force of air resistance balances the downward force of gravity, resulting in a net force of zero and constant velocity.

To account for the changing acceleration and terminal velocity, the "Suvat" equations (also known as the kinematic equations) can be modified. The modified equations take into consideration the air resistance and the concept of terminal velocity. Here's an adjusted equation for the vertical motion of an object falling with air resistance:

$v=u+(gt-\frac{kv}{m})$

where:

• $v$ is the final velocity
• $u$ is the initial velocity
• $g$ is the acceleration due to gravity
• $t$ is the time
• $k$ is a constant related to the shape and properties of the falling object and the medium through which it is falling
• $m$ is the mass of the object

In this equation, the term $\frac{kv}{m}$ represents the force of air resistance, which is proportional to the velocity $v$ and acts in the opposite direction of motion. As the object's velocity increases, the force of air resistance also increases until it balances the force of gravity, resulting in zero net force and a constant terminal velocity.

It's important to note that the specific form of the equation and the values of $k$ and $m$ will depend on the object and the medium through which it is falling. These values can be determined experimentally or estimated based on known properties.