The function $v(t)=t^3-10t^2+24t$ on $0,8,$ is the velocity in $\frac{m}{s}$ of an object moving along a line with the given velocity v$.$ Assume time t is measured in seconds.

a$.$ Determine when the motion is in the positive direction and when it is in the negative direction.

b$.$ Find the displacement over the given interval.

c$.$ Find the distance traveled over the given interval.

A$.$ For $t-$values in the interval$($s$)$

$($Type your answer in interval notation. Use a comma to separate answers as needed.$)$

B$.$ The motion is never in the positive direction.

When is the motion in the negative direction? Select the correct choice and, if necessary, fill in the answer box to complete your choice.

A$.$ For $t-$values in the interval$($s$).$

$($Type your answer in interval notation. Use a comma to separate answers as needed.$)$

B$.$ The motion is never in the negative direction.

b$.$ Find the displacement over the given interval.

The displacement over the given interval is $$ m$.$

$($Simplify your answer.$)$

c$.$ Find the distance traveled over the given interval.

The distance traveled over the given interval is $$ m$.$

$($Simplify your answer.$)$