What are the dimensional units of #A# and #B# if a volume, #V#, is given by the equation #V=A*t^3+B/t#?

1 Answer
Mar 19, 2016

Answer:

#A# is #L^3/T^3# and #B# is #L^3*T#

Explanation:

Any volume can be expressed as cubic length, #L^3#

Only adding up cubic lengths on the right will give the result of another cubic length on the left (Note: multiplying terms would not do this).

So, given #V=A*T^3+B/T#, let

#A*T^3=L^3# meaning the first term is a volume (cubic length), and
#B/T = L^3# meaning the second term is also a volume.

Finally we just solve for the respective letters, #A# and #B#.

#A=L^3/T^3#
#B=L^3*T#