Question

(a) The displacement `s` of a particale in time `t` related as `s = alpha + beta t + gamma t^(2) + delta t^(2)`
(b) The veloctiy `v` of particle varies with time as
`v = alpha t + beta t^(2) + (gamma )/(t + s)`
Findk the dimension fo `alpha, beta, gamma` and `delta`.

Answer 1

(a) Dimensions of each term on the right-hand side have same dimension as that fo `s`, i.e., `[L]`
`[alpha] = L`
`[beta t] = L implies [beta] = LT^(-1)`
`[gamma t^(2)] = L implies [gamma] = LT^(-2)`
`[delta t^(2)] = L implies [delta] = LT^(-3)`
(b) Dimension of each term on the right-hand side have same dimensions as that of `v`, i.e., `[Lt^(-1)]`
`[alphat] = Lt^(-1) implies [alpha] = LT^(-2)`
`[beta t^(2)] = LT^(-1) implies [beta] = LT^(-3)`
`[delta] = L`
`[(gamma)/(t + S)] = LT^(-1) implies [gamma] = L`