Answer
Equations (a) is wrong while (b) and (c) could possibly be correct.
Work Step by Step
(a) $x =vt^2 + 2at$
Let's check the dimensions on the right side of the equation.
$\frac{[L][T]^2}{[T]} + \frac{[L][T]}{[T^2]} = \frac{[L]}{[T]}$
This could not be correct because the dimensions of $x$ should be [L].
(b) $x =v_0t + \frac{1}{2}at^2$
Let's check the dimensions on the right side of the equation.
$\frac{[L][T]}{[T]} + \frac{[L][T]^2}{[T]^2} = [L]$
This could be correct because the dimensions of $x$ should be [L].
(c) $x =v_0t + 2at^2$
Let's check the dimensions on the right side of the equation.
$\frac{[L][T]}{[T]} + \frac{[L][T]^2}{[T]^2} = [L]$
This could be correct because the dimensions of $x$ should be [L].
