While the blocks are moving, what is the tension T in the rope to connect the two blocks? What is the mass of block B?

Question

Two blocks connected by a light horizontal rope sit at rest on a horizontal, frictionless surface. Block A has mass 15.0kg, and block B has mass m. In the first 5.00s after the force is applied, block A moves 18.0 m to the right. While the blocks are moving, what is the tension T in the rope to connect the two blocks? What is the mass of block B?

Answer 1

from x = 0.5(a)(t^2),  we have 18 = 0.5(a)(5^2) = 0.5(25)a,

or a = 2(18)/25 = 36/25 m/s^2;  then, if T = tension in rope attached to block A, then T = 15(a) = 15(36)/25 = 108/5 Newtons = 21.6 Newtons;  if F denotes the applied force (applied to block B),

then:  F - T = ma;  or F - 21.6 = m(36/25);  to solve for m, it looks as though we need F;  do we know F?