Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [b]}$$
The bar reaches a terminal speed when the net force exerted on it is zero.
We have a magnetic force due to the original flux. This force direction is to the right since the battery's current direction is clockwise (which means its direction in the bar is southward).
So the bar starts to move to the right without friction (we assumed that the bar and the rails are frictionless). This means that the area of the loop increases and that increases the flux.
This change in flux causes an induced emf and an induced emf that fights this change. So according to Lenz's law, the direction of the induced current in the loop is counterclockwise. Hence, the direction of the current in the bar is northward.
This induced emf will create a magnetic force exerted on the loop to the left, the induced force increases with time until it becomes equal to the original magnetic force.
Then the bar moves at a constant speed which is the terminal speed.
Now Let's talk mathematically, at terminal speed the battery emf equals the induced emf.
$$\varepsilon_{\rm induced} =\varepsilon_{\rm battery}$$
$$\varepsilon_{\rm battery}=Blv_{\rm term} $$
$$\boxed{v_{\rm term} =\dfrac{\varepsilon_{\rm battery}}{Bl}}$$
$$\color{blue}{\bf [b]}$$
Plug the given into the boxed formula,
$$ v_{\rm term} =\dfrac{(1) }{ (0.5)(0.06)}=\color{red}{\bf 33.3}\;\rm m/s $$
