The acceleration of an object (in \( \mathrm{m} / \mathrm{s}^{2} \) ) is given by the function \( a(t)=8 \sin (t) \). The initial velocity of the object is \( v(0)=-10 \mathrm{~m} / \mathrm{s} \). Round your answers to four decimal places. a) Find an equation \( v(t) \) for the object velocity. \[ v(t)= \] \( \square \) b) Find the object's displacement (in meters) from time 0 to time 3 . \( \square \) meters c) Find the total distance traveled by the object from time 0 to time 3 .
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Step 1: To find the velocity function \( v(t) \), integrate the acceleration function \( a(t) = 8 \sin(t) \). Show more…
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