Velocity v is given by v = at2 + bt + c, where t is time. What are the dimensions of a, b and c, respectively?

Dimensions of velocity are [v] = [L][T-1]So, dimensions of [at2] = [LT-1]⇒ [a]T2=LT-1[a]=LT-3 Dimensions of [bt]=LT-1⇒[b][T]=LT-1⇒  [b]=LT-2 Dimensions of [c]=LT-1