A particle can be described as $v=24t^{2}6t-5,in\frac{m}{sec}.$ The particle is located at the origin when $t=0.$

Find the acceleration as a function of time

Find the position $x$ as a function of time

Find the positions of the particle at $t=2$ and $t=5sec$

Find the average velocity of the particle between $2$ sec and $5$ sec $.$

Toss an object vertically upward at $30\frac{m}{s}$ from the top of a building that is $40$ m high. Find the total time in the air. You must use the quadratic equation method to solve it

Given vector

$6.$ Find the dot product

$7.$ Find the cross product

$8.$ Find the angle between two vectors

$9.$ Find the angle between vector a and the $x-$axis.

$10.$ If find the value of $y,$ so that the vector $c$ is perpendicular to vector a