Motion Equations Analysis

Equations of motion are fundamental formulas used in physics to describe the movement of objects. These equations typically relate displacement, velocity (initial and final), acceleration, and time for objects moving under constant acceleration.

Statement I: u = v + at Analysis

Statement I is given as u = v + at. This equation can be rearranged to solve for the final velocity ($v$):

$$ u = v + at $$

Subtracting '$at$' from both sides gives:

$$ u - at = v $$

Or equivalently,

$$ v = u - at $$

This form is related to the standard first equation of motion, which is typically written as $v = u + at$. The equation $v = u - at$ correctly describes motion where the acceleration is constant and negative (i.e., deceleration). However, the way statement I is presented ($u = v + at$) is not the standard or most common representation used to define the relationship between initial velocity, final velocity, acceleration, and time. Questions often test the recognition of these standard forms.

Statement II: 2as = v^2 - u^2 Analysis

Statement II is given as 2as = v^2 - u^2. This equation relates final velocity ($v$), initial velocity ($u$), acceleration ($a$), and displacement ($s$). It can be rearranged to the more commonly recognized form:

$$ v^2 = u^2 + 2as $$

This is a standard and widely used kinematic equation derived for motion with constant acceleration. It is one of the core equations describing how velocity changes over distance in the absence of time.

Conclusion on Motion Equations

Comparing the two statements with the standard kinematic equations:

• Statement II ($v^2 = u^2 + 2as$) is a correct and standard equation of motion.
• Statement I ($u = v + at$), while algebraically related to a valid motion scenario ($v = u - at$), is not presented in the conventional format ($v = u + at$) and might be considered incorrect or non-standard in the context of identifying primary equations of motion.

Therefore, based on the typical conventions in physics education, only statement II is considered a standard equation of motion.