Question

The distance covered by a particle in time t is given by `x=a+bt+ct^2+dt^3`, find the dimensions of a,b,c and d.

Answer 1

The equation contains five terms. All of them should have the same dimensions . Since `[x]=` length, each of the remaining four must have the dimension of length .
Thus, `[a] = ` length `= L`
`[bt] = L ` , or `[b] = LT ^(-1)`
`[ct^(2)] =L ` , or `[c] = LT^(-2)`
and `[dt^(3)] =L ` or `[d] = LT^(-3)`