at = Dimension of v i,e., [LT-1]
or, a = [LT-1]/t = [LT-1]/T = [LT-2]
t + c = time
Hence, c = Dimension of time = [T]
(Because only like quantities can be added)
Now, b/t + c = v
Hence, b = v x time = [LT-1] [T] =[LT-1] [T]
or, b = [L]
And a = [LT-2], [b = L] and c = [T].