Answer
$\frac{v^{2}}{x}$, $\frac{x}{t^{2}}$ and $\frac{v}{t}$ have the dimension of an acceleration.
Work Step by Step
Dimension of t (time): [T].
Dimension of x (distance): [L].
Dimension of v (velocity): $\frac{[L]}{[T]}$.
Dimension of an acceleration: $\frac{[L]}{[T^{2}]}$.
(a) $xt^{2}=[L][T^{2}]$.
$xt^{2}$ has not the dimension of an acceleration.
(b) $\frac{v^{2}}{x}=\frac{(\frac{[L]}{[T]})^{2}}{[L]}=\frac{\frac{[L^{2}]}{[T^{2}]}}{[L]}=\frac{[L]}{[T^{2}]}$.
$\frac{v^{2}}{x}$ has the dimension of an acceleration.
(c) $\frac{x}{t^{2}}=\frac{[L]}{[T^{2}]}$.
$\frac{x}{t^{2}}$ has the dimension of an acceleration.
(d) $\frac{v}{t}=\frac{\frac{[L]}{[T]}}{[T]}=\frac{[L]}{[T^{2}]}$.
$\frac{v}{t}$ has the dimension of an acceleration.
