The acceleration of an object is given by the function $a(t)=8sint.$ The initial velocity of the object is $v(0)=-2\frac{m}{s}.$ Round your answers to four decimal places.

$($a$)$ Determine the equation for the object's velocity.

$($b$)$ Determine the object's displacement from $0$ seconds to $3$ seconds. Round to the nearest whole meter.

$($c$)$ Determine the total distance traveled by the object from $0$ seconds to $3$ seconds. Round to the nearest whole meter.

Please hurry i only have $2$ hours