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

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.