University Physics Volume 1 — Mechanics · Problem 51

Units and Measurement — OpenStax

Physics — University · dimensional-analysis

Problem

Consider the physical quantities

s

v

a

, and

t

with dimensions

[s] = L

[v] = LT^{-1}

[a] = LT^{-2}

, and

[t] = T

. Determine whether each of the following equations is dimensionally consistent. (a)

v^2 = 2as

; (b)

s = vt^2 + 0.5at^2

; (c)

v = s/t

; (d)

a = v/t