1.4 Exercise 4

Consider the physical quantities s, v, a, and t with dimensions $\left[s\right] = \text{L} ,$ $\left[v\right] = \text{LT}^{−1} ,$ $\left[a\right] = \text{LT}^{−2} ,$ and $\left[t\right] = \text{T} .$ Determine whether each of the following equations is dimensionally consistent. (a) $v^{2} = 2 a s ;$ (b) $s = v t^{2} + 0.5 a t^{2} ;$ (c) $v = s / t ;$ (d) $a = v / t .$