How to get the time and the amount of force if the only given are mass and velocity?

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The impulse J is defined as the integral `int_(t_1)^(t_2) F dt` where `t_1,t_2` defines the time interval, F is the force and we are integrating with respect to time.

Now `F=(dp)/(dt)` where p is the momentum. So we have `int_(t_1)^(t_2) F dt=int_(p_1)^(p_2) (dp)/(dt) dt=Delta p`

Also `J=F Delta t=m Delta v=mv_1-mv_0=Delta p`

So I assume in your problem you are given the constant mass and the initial and terminal velocity. (Note that the force F and the mass m are required to be constant in these equations.)

Then you can compute the impulse from the mass and the initial,terminal velocities. Knowing the impulse will not give you the force nor the time interval -- there would have to be some other information given.

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