I have object with a given mass $m$, which is moving with the velocity $v$ and there is force $\bf F$ pushing against movement of the object.
How far will object travel until it stops and how long will it take?
Feel ashamed I have to ask for this easy problem, but I just cannot find solution.
Thanks for any help.
You can simply apply this formula that describes the accelerated motion. $$x(t)=x_0+v_0t+\frac{1}{2}at^2$$ Where $x(t)$ is the position depending on time and this determinates how far the object goes, $x_0$ is the initial position, $v_0$ the initial velocity and then $a$ is the acceleration you can calculate with Motion Equation (Newton's second law). You know the force and the mass so you can use the Newton's second law: $$\vec{F}=m\vec{a}$$ Pay attention on the sign of the acceleration that is against the velocity as you said. Once you have found the acceleration, you know that $\vec{v}=\vec{a}t$ and so you have the time. Put this time in the first equation and have how far it goes. Hope this can help you!
