The given equation describes the _________ relation.

$s = ut +\frac{1}{2}at^2$

position-time

The correct answer is option 1. position-time.

The given equation, \(s = ut + \frac{1}{2}at^2\), is a fundamental equation in classical mechanics that describes the relationship between an object's position (\(s\)) and time (\(t\)) when the object is undergoing constant acceleration (\(a\)).

Here's a breakdown of each term in the equation

\(s\) represents the position or displacement of the object at a specific time \(t\). It's essentially telling us how far the object has traveled from its initial position.

\(u\) represents the initial velocity of the object at \(t = 0\). This is the velocity of the object at the starting point of our observation.

\(a\) represents the constant acceleration of the object. This could be due to gravity, friction, or any other force acting on the object. Importantly, it's assumed to be constant throughout the motion.

\(t\) represents the time elapsed since the object started its motion.

The equation combines two components of the object's motion:

1. Initial Motion: The term \(ut\) represents the distance traveled during the initial motion when the object was moving at a constant velocity \(u\) for a time \(t\).

2. Acceleration: The term \(\frac{1}{2}at^2\) represents the additional distance traveled due to the object's acceleration over time \(t\). This term arises from the kinematic equation \(s = ut + \frac{1}{2}at^2\), which describes the distance traveled under constant acceleration.

By adding these two components, we get the total displacement or position of the object at time \(t\).

This equation is often used in physics and engineering to analyze the motion of objects under constant acceleration. It's particularly useful for predicting the position of an object at any given time, given its initial conditions and the constant acceleration acting upon it