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A particle moves on a coordinate line with an acceleration at time t seconds of e^t/2 m/sec^2. At t=0 the particle is at the origin, and its velocity is -4 m/sec

A particle moves on a coordinate line with an acceleration at time t seconds of et2 msec2 At t0 the particle is at the origin and its velocity is 4 msec class=

Respuesta :

caylus
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]



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