Hello,
A) [tex]a=e^ \frac{t}{2} \\\\
v(t)=\int\ a\ dt=\int\ e^ \frac{t}{2}\ dt=2*e^ \frac{t}{2}+C\\\\v(0)=-4\\
2*e^ \frac{0}{2}+C=-4\\
C=-6\\\\
\boxed{v(t)= 2*e^ \frac{0}{2}-6}\\\\
[/tex]
B)
[tex]2*e^ \frac{t}{2}-6=0\\\\
e^ \frac{t}{2}=3\\\\
t=2*ln(3)\approx{2,19722...}\\
[/tex]
C)
[tex]x(t)=\int_0^6(2*e^ \frac{t}{2}-6})\ dt=\left[4*e^ \frac{t}{2}-6t\right]_0^6\\\\ =e^3-36-4=4e^3-40\approx{40.3421...}\\\\[/tex]
