Velocity `v` is given by `v=at^(2)+bt+c`, where `t` is time. What are the dimensions of `a, b and c` respectively?

Options

A. `["LT"^(-3)],["LT"^(-2)]and["LT"^(-1)]`
B. `["LT"^(-1)],["LT"^(-2)]and["LT"^(-3)]`
C. `["LT"^(-2)],["LT"^(-3)]and["LT"^(-1)]`
D. `["LT"^(-1)],["LT"^(-3)]and["LT"^(-2)]`

Answer

A

Explanation

Dimensions of velocity are `["V"]=["L"]["T"^(-1)]`
So, deminsions of `["at"^(2)]=["LT"^(-1)]`
`rArr" "["a"]["T"^(2)]=["LT"^(-1)]`
`rArr" "["a"]=["LT"^(-3)]`
Dimensions of `["bt"]=["LT"^(-1)]rArr["b"]["T"]=["LT"^(-1)]`
`rArr" "["b"]=["LT"^(-2)]`
Dimensions of `["c"]=["LT"^(-1)]`