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The acceleration of an object (in m/s2) is given by the function a ( t ) = 6 sin ( t ) a(t)=6sin(t). The initial velocity of the object is v ( 0 ) = − 2 v(0)=-2 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity.

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boffeemadrid

Answer:

[tex]v(t)=-6cos(t)+4[/tex]

Explanation:

We have acceleration given by

[tex]a(t)=6sin(t)[/tex]

Velocity at t = 0

[tex]v(0)=-2\ m/s[/tex]

Velocity is given by

[tex]v(t)=\int a(t)dt\\\Rightarrow v(t)=\int 6sin(t)dt\\\Rightarrow v(t)=6\int sin(t)\\\Rightarrow v(t)=-6cost+C[/tex]

at t = 0

[tex]-2=-6cos0+C\\\Rightarrow -2+6=C\\\Rightarrow C=4[/tex]

The equation will be

[tex]\mathbf{v(t)=-6cos(t)+4}[/tex]

onyebuchinnaji

The equation for the velocity of the object is written as [tex]v(t) = -6 \ cos(t) \ + \ 4[/tex]

The given parameters;

  • acceleration of the object, a(t) = 6 sin(t)
  • initial velocity, v(0) = -2 m/s

The equation for the object's velocity is calculated as follows;

[tex]v(t) = \int\limits {a(t)} \, dt \\\\v(t) = \int\limits {6 \ sin(t)} \, dt\\\\v(t) = 6\int\limits {sin(t)} \, dt\\\\v(t) = -6\ cos(t) \ + \ C[/tex]

when t = 0, v = -2 m/s;

[tex]-2 = -6 \ cos(0) \ + \ C\\\\-2 = -6 + C\\\\C = 4[/tex]

The equation for the velocity of the object is written as;

[tex]v(t) = -6 \ cos(t) \ + \ 4[/tex]

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