91Ó°ÊÓ

When we talk about the speed of an object at a specific instant, we refer to it as its 'instantaneous velocity'. Unlike average velocity, which considers the total distance covered over a period of time, instantaneous velocity focuses on a particular moment. It is the velocity that a speedometer reads at any given time.

Imagine dropping a ball from a certain height. As it falls, its speed increases moment by moment. The velocity of the ball at any particular moment during its fall is its instantaneous velocity. It is crucial in physics to understand that this velocity involves both magnitude (how fast the object is moving) and direction (where it is going).

For a body in free fall where gravity is the only force at work (ignoring air resistance), the formula for calculating instantaneous velocity at any given time is simple. As the body accelerates, its instantaneous velocity after time 't' seconds is given by the expression \(v = gt\), where \(g\) represents the acceleration due to gravity and is approximately 9.8 \(\text{m/s}^2\) on Earth's surface. This formula assumes the body starts from rest and that the direction of gravitational acceleration is considered positive.

Gravity is a force that draws objects toward the Earth's center, creating an 'acceleration' known as the acceleration due to gravity, symbolized by \(g\). On Earth, this value is roughly 9.8 \(\text{m/s}^2\) near the surface, meaning that for each second an object is in free fall, its speed increases by approximately 9.8 meters per second.

This acceleration is what causes a ball thrown up in the air to slow down, stop at its peak, and then speed up again on its way down. It's important to note that the value of \(g\) is an average and can vary slightly depending on altitude and geographical location.

Why is \(g\) Constant?

Acceleration due to gravity is considered constant near Earth's surface because the change in distance from the Earth's center over the scale of human activities is very small relative to the Earth's radius, making \(g\)'s variation negligible for most practical purposes.

Free fall is an intriguing concept in physics, where a body moves under the influence of gravity alone, with no other forces, like air resistance, acting on it. In this idealized situation, all objects, regardless of their mass, fall at the same rate because the acceleration due to gravity is constant.

For an object in free fall, its motion can be predicted and described by kinematic equations. If we ignore air resistance and presume that the acceleration \(g\) is constant throughout the fall, we have a uniformly accelerated motion where the speed of the object increases at a steady rate.

Visualizing Free Fall

To help visualize the motion of a body in free fall, picture an object dropped from a height above the ground. As it falls, every second, its instantaneous velocity increases due to the constant acceleration of gravity. There's no initial velocity if it was simply dropped (not thrown), so the velocity at any point is simply the product of acceleration and time elapsed. The path of the object is a straight line, and its speed increases by about 9.8 \(\text{m/s}\) every second, demonstrating free fall's characteristic of constant acceleration.