A block of mass $1\ \text{kg}$ rests on a plank of mass $3\ \text{kg}$, which lies on a smooth floor. The coefficient of friction between the block and the plank is $0.4$, both for sticking and for sliding. From $t = 0$, a horizontal force $F = bt$, with $b = 2\ \text{N/s}$, pulls the block, as shown in the figure. Take $g = 10\ \text{m/s}^2$. Which of the following statements are correct?

Fig. 1: A plank of 3 kg lies on a smooth floor, with a block of 1 kg on it near its middle. The friction coefficient between block and plank is 0.4, and a horizontal force F equal to b t pulls the block to the right.