Understanding the fundamental equations of motion is crucial in physics, especially when dealing with objects moving with constant acceleration. These equations describe the relationship between initial velocity (\(u\)), final velocity (\(v\)), acceleration (\(a\)), time (\(t\)), and displacement (\(s\)).

Motion Equations Overview

The three primary equations of motion for objects moving with constant acceleration are:

• \(v = u + at\)

  This equation of motion relates final velocity, initial velocity, acceleration, and time. It tells us how velocity changes over a period due to constant acceleration.

• \(s = ut + \frac{1}{2}at^2\)

  This equation of motion describes the displacement of an object based on its initial velocity, acceleration, and time. It helps calculate how far an object travels.

• \(v^2 = u^2 + 2as\)

  This equation of motion connects final velocity, initial velocity, acceleration, and displacement. It is particularly useful when time is not known or not required in the calculation.

Analyzing Given Options for Equations of Motion

Let's examine each provided option to identify which one is not a standard equation of motion:

• Option 1: \(2as = v^2 - u^2\)

  This equation can be rearranged to \(v^2 = u^2 + 2as\). This is clearly one of the standard equations of motion. It shows the relationship between final velocity, initial velocity, acceleration, and displacement.

• Option 2: \(s = v - u\)

  This expression relates displacement (\(s\)) to the difference between final velocity (\(v\)) and initial velocity (\(u\)). However, this is not a standard equation of motion. In kinematics, displacement depends on initial velocity, acceleration, and time, or final velocity, acceleration, and time, or both velocities and time. A simple difference of velocities does not directly represent displacement in the context of constant acceleration where time and acceleration terms are crucial.

• Option 3: \(v - u = at\)

  This equation can be rearranged to \(v = u + at\). This is also one of the fundamental equations of motion, linking final velocity, initial velocity, acceleration, and time.

• Option 4: \(s = ut + \frac{at^2}{2}\)

  This equation is exactly \(s = ut + \frac{1}{2}at^2\), which is a core equation of motion describing displacement based on initial velocity, acceleration, and time.

Identifying Non-Standard Motion Equation

Based on our analysis, the expression \(s = v - u\) does not align with any of the established equations of motion used in kinematics for constant acceleration. While \(v-u\) represents the change in velocity, it does not represent displacement directly in the context of these equations. Displacement involves distance covered over time under specific acceleration conditions, not merely a difference in speeds.

Therefore, \(s = v - u\) is not an equation of motion.