The time taken to reach the velocity 2v is 2fv/m. Acceleration is the term used to describe the change in a moving object's velocity with relation to time.
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
It is given that the force acting on the particle is F. So from Newton's law of motion;
F = ma
a =f/m
dv/dt = f/m
[tex]\int\limits^2_0{} \, dv \\[/tex][tex]= \int\limits^l_0 {f/m} \, dt[/tex]
2v = f/m * t
t = 2fv / m
Hence the time taken to reach the velocity 2v is 2fv / m
To learn more about velocity refer:
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