Solve the following problems using the equations of motion with acceleration constant. Present your procedure in detail to receive partial points. Explain each step and show your c$\mathrm{on}$glasses$.$

Equation problems$\mathrm{from}$speed n:

$1.$ A car starts from rest and accelerates uniformly at$\mathrm{ 4}\hspace{0.17em}$m$/$s during$\mathrm{ 6}\hspace{0.17em}$s$.$ Calculate its final speed.

$2.$ A train is moving with an initial speed of $20\hspace{0.17em}$m$/$s$\mathrm{²}$ and experiences an acceleration constant of$\mathrm{ 2}\hspace{0.17em}$m$/$s$\mathrm{²}$ during $5\hspace{0.17em}$s$.$What is its final speed?

$3.$ An airplane takes off from the ground with an acceleration$\mathrm{from}$n constant of$\mathrm{ 3}\hspace{0.17em}$m$/$s$\mathrm{²}$ and an initial speed of$50\hspace{0.17em}$m$/$s$.$How long does it take to reach a speed of$100\hspace{0.17em}$m$/$s$?$

$4.$ A car accelerates uniformly from rest at a rate of$\mathrm{ 2}\hspace{0.17em}$m$/$s$\mathrm{²}$ during $5\hspace{0.17em}$s$.$ What is its initial velocity?