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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).enter image description here

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    $\begingroup$ $v=u + Ft/m$ I have combined two common equations $F=ma$ and $v=u+at$. Here $t=2$ and $u=0$ $\endgroup$
    – Satya
    Sep 15 at 5:00
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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 $$F=5m \ \text {Newton}$$

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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. $$F=mv/t$$

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