The velocity `upsilon` of a particle depends upon time t, according to the equation `upsilon = a+ bt +(c )/(d +t)` Write the dimensions of a,b,c, and d.

Explanation

From principle of homogeneity
`[a]=[v] or [a]=[LT^(-1)]`
`[bt]=[v]`
or `[b]=([v])/([t])=([LT^(-1)])/([T])` or `[b]=[LT^(-2)]`
Similarly, `[d]=[t]=[T]`
Further, `([c])/([d+t])=[v]` or `[c]=[v][d+t]`
or `[c]=[LT^(-1)][T]`
or `[c]=[L]`
`therefore` Dimensions of `a=[LT^(-1)]`
Dimensions of `b=[LT^(-2)]`
Dimensions of `d=[L]`
Dimensions of `d=[T]`