Plotting the graph of Friction Force vs. time (Laws of motion)

[SpectraPhy09]

Homework Statement

Coefficient of friction between all the surfaces in 0.5. Which diagram would describe the friction between the ground and the 2Kg Block when f = t N is applied on the 2kg Block? It is given that the string is not taut initially.(Plz check the the diagram in the image attached). take g= 10m/s^2

Relevant Equations

F = ma
F(friction) = μmg

F.B.D Of first block
(I have shown only the horizontal Forces)

f1(max) = μ (1kg)(g) = 0.5 * 10 = 5N
F.B.D Of the second Block

f2(max) = μ (3kg)(g) = 15N

Now the string will become taut and the tension will start acting when f = t = 5N
But for 0<f<5N there will be no motion between the 1 kg and the 2 kg block so the f2=0
but when f > 5N the string will become taut and the friction the Tension will start will acting now suppose the acceleration of the 1 kg block in left direction is a1 then,
(1)a1 = f - T - f1
and suppose the acceleration od the 2kg block is a2 then,
(2)a2 = f1 - f2 - T
But how will be plot the graph between f2 and t after t=5 since we do not know the T ension neither the acceleration of the block.
Also in the option for 0<t<5 there is different graph that mine.
Plz can someone help me how to solve this problem ahead?

 

[haruspex]

But for 0<f<5N there will be no motion between the 1 kg and the 2 kg block so the f2=0

If f2=0 and the string is not taut, what stops the pair of blocks moving left?

suppose the acceleration od the 2kg block is a2

If the 2kg block is moving, what is the state of the string? Assume it is inextensible.

(2)a2 = f1 - f2 - T

You have drawn f1 and f2 acting in the same direction on the 2kg block.