Equation `s_t=u + at - 1/2 a` does not seem dimensionally correct, why?

With the usual notations , check if the following equation S_(t) = u + (1)/(2) a ( 2t -1) is dimensionally correct or not.

With the usual notations , check if the following equation S_(t) = u + (1)/(2) a ( 2t -1) is dimensionally correct or not.

Assertion: The given equation x = x_(0) + u_(0)t + (1)/(2) at^(2) is dimensionsally correct, where x is the distance travelled by a particle in time t , initial position x_(0) initial velocity u_(0) and uniform acceleration a is along the direction of motion. Reason: Dimensional analysis can be used for cheking the dimensional consistency or homogenetly of the equation.

Assertion: The given equation x = x_(0) + u_(0)t + (1)/(2) at^(2) is dimensionsally correct, where x is the distance travelled by a particle in time t , initial position x_(0) initial velocity u_(0) and uniform acceleration a is along the direction of motion. Reason: Dimensional analysis can be used for cheking the dimensional consistency or homogenetly of the equation.

Check whether equation F.S. = 1/2 mv^2 -1/2 m u^2 is dimensionally correct, where m is mass of the body, v its final velocity, u its initial velocity, F is force applied and S is the distance moved.

Show that the equation s = ut + frac(1)(2)at^2 is dimensionally correct.

Show that the equation V = u + at is dimensionally correct.

A dimensionally correct equation need not be actually correct, but a dimensionally incorrect equation is necessarily wrong. Justify.

Assertion : All equations which are physically correct must also be dimensionally correct. Reason : All equations which are dimensionally correct must also be physically correct.