# Force from time and velocity

Let's say I have a goal velocity $$(v)$$. In $$n$$ amount of time $$(t)$$ (let's say two seconds). What is the formula for finding the amount of force I would need (not counting other forces like drag/friction) to accelerate to velocity $$v$$ by time $$t$$ ? (in this case let's say 2 seconds). (see figure for example).

• $v=u + Ft/m$ I have combined two common equations $F=ma$ and $v=u+at$. Here $t=2$ and $u=0$ Sep 15 at 5:00

The equation you would use is $$v=v_0+at$$ Note that the constant acceleration can be expressed as $$a=\frac{F}{m}$$ if the object has a mass $$m$$. So $$v=v_0+\frac{F}{m}t$$ and so $$F=\frac{m(v-v_0)}{t}$$ and if the initial velocity is zero then $$F=\frac{mv}{t}$$ So if $$t=2s$$ then $$F=\frac{mv}{2}$$ If your target velocity is for example $$10ms^{-1}$$, then $$F=5m \ \text {Newton}$$
Impulse $$\vec J$$ imparted by force $$\vec F$$ will be equal to the change in momentum $$\Delta \vec p$$. $$d\vec J=\vec Fdt$$. Force being constant $$\vec J=\vec Ft$$. $$\Delta \vec p=m\vec v=\vec J$$ which gives us. $$F=mv/t$$