Velocity after t seconds with a time varying Force

[Physics lover]

Homework Statement

I am writing the statement of problem here but its figure is in Attempt at a solution.
A 1kg block moving on horizontal rough surface of friction coefficient 0.6 is pushed with a force varying with time t in seconds as shown in figure.If initial velocity of block was 4.5 m/s.Find the velocity (in m/s) at t= 3 s.

Relevant Equations

F=Ma
dv/dt=a

Figure given in question-:

I first found out the time when force will be equal ro friction.After force becomes equal to friction there will be no acceleartion further,so velocity after that time will be same.I calculated the velocity by getting a relation of it with time.I got the velocity as 6m/s.But the answer given is 0 m/s.I can't get it.Please help.

 

[BvU]

so velocity after that time will be same

Meaning the friction miraculously disappears ?

 

[Physics lover]

Meaning the friction miraculously disappears ?

No i meant that after force becomes equal to friction,friction will balance force.
For eg:If force is 3 N friction will adjust itself to 3 N.

 

[Merlin3189]

If the question had not mentioned any force pushing the block, only friction retarding it, then what would happen to the block?
It is moving at 4.5 m/s across this rough surface: does it continue moving at 4.5 m/s? does it suddenly stop dead? or what?

 

[ehild]

No i meant that after force becomes equal to friction,friction will balance force.
For eg:If force is 3 N friction will adjust itself to 3 N.

No, the friction stays the same till the block moves. If it is greater than the pushing forces the block will decelerate.

 

[Flatlanderr]

Although there's more than one way to do it, the problem's listed under "Momentum", so knowing the momentum form of Newton's second law,
$$
F = \frac{dp}{dt}
$$
think about how to solve for the final velocity given the push force (as a function of time) and the frictional force (a constant function of time).