Answer:
v=4m/s
Explanation:
The formulas for accelerated motion are:
[tex]v=v_0+at\\x=x_0+v_0t+\frac{at^2}{2}[/tex]
We can derive the formula [tex]v^2=v_0^2+2ad[/tex] from them.
We have:
[tex]v-v_0=at\\t=\frac{v-v_0}{a}[/tex]
And substitute:
[tex]x=x_0+v_0(\frac{v-v_0}{a})+\frac{a}{2}(\frac{v-v_0}{a})^2\\x-x_0=\frac{v_0(v-v_0)}{a}+\frac{(v-v_0)^2}{2a}\\2a(x-x_0)=2v_0(v-v_0)+(v-v_0)^2=2v_0v-2v_0^2+v^2+v_0^2-2vv_0=v^2-v_0^2[/tex]
Where in the first step of the last row we just multiplied everything by 2a. Since [tex]x-x_0[/tex] is the displacement d, we have proved that [tex]v^2=v_0^2+2ad[/tex]
We use then our values to calculate the final velocity when starting from rest, traveling a distance 0.002m with acceleration [tex]4000 m/s^2[/tex]:
[tex]v=\sqrt{v_0^2+2ad}=\sqrt{2(4000m/s^2)(0.002m)}=4m/s[/tex]
