Velocity of a particle at time t is given by `v=at+(b)/(t+c)a,b`, care constant. The dimension of a b, c will be ......

Options

A. `L^(2),T and LT^(-2)`
B. `LT^(2),LT and L`
C. `L,LT and T^(2)`
D. `LT^(2), L and T`

Explanation

`v=at+(b)/(t+c)`
Hence both term on right hand side should have dimension of velocity.
`:.v=at`
`:.a=(v)/(t)`
`:.[a]=([v])/([t])`
`=(LT^(-1))/(T)`
`=LT^(-2)` By homogeneity indicate,
and `v=(b)/(t+c)=(b)/(t) " " t+c`(has dimension of time)
`:.b=vt " " c=t`
`:.[b]=[v][t] :. [c]=[t]`
`=(LT^(-1))(T) " " :. c=T`
`=L`
`:.[a],[b],[c]=LT^(-2), L and T`