What is the isolated variable for u in the equation s = ut + 1/2 at²?

What is the isolated variable for u in the equation s = ut + 1/2 at²?

• A. √[s - (at / 2)]
• B. [s - (at² / 2)] / t
• C. 2 / (sat)
• D. s - 1/2 at² - t

Answer: (B)

In the equation \( s = ut + \frac{1}{2} at^2 \), the goal is to isolate the variable \( u \). To achieve this, the equation needs to be manipulated so that \( u \) is expressed in terms of \( s \), \( a \), and \( t \). Starting from the original equation, we can rearrange it by first subtracting the term \(\frac{1}{2} at^2\) from both sides: \[ s - \frac{1}{2} at^2 = ut. \] Now, to isolate \( u \), divide both sides of the equation by \( t \): \[ u = \frac{s - \frac{1}{2} at^2}{t}. \] The result accurately derives the value of \( u \) in relation to \( s \), \( a \), and \( t\), confirming that option B, which presents the equation in that isolated form, is the correct choice. This isolates \( u \) effectively by logical steps of algebraic manipulation, leading to the straightforward format required for interpretation, validation, or further calculations in the context of kinematic equations.

In the equation ( s = ut + \frac{1}{2} at^2 ), the goal is to isolate the variable ( u ). To achieve this, the equation needs to be manipulated so that ( u ) is expressed in terms of ( s ), ( a ), and ( t ).

Starting from the original equation, we can rearrange it by first subtracting the term (\frac{1}{2} at^2) from both sides:

[ s - \frac{1}{2} at^2 = ut. ]

Now, to isolate ( u ), divide both sides of the equation by ( t ):

[ u = \frac{s - \frac{1}{2} at^2}{t}. ]

The result accurately derives the value of ( u ) in relation to ( s ), ( a ), and ( t), confirming that option B, which presents the equation in that isolated form, is the correct choice. This isolates ( u ) effectively by logical steps of algebraic manipulation, leading to the straightforward format required for interpretation, validation, or further calculations in the context of kinematic equations.