A particle moves so that its position vector varies with time as $\overrightarrow{r}=A\cos \omega t\hat{\mathrm{i}}+A\sin \omega t\hat{\mathrm{j}}$. Find the,

$\left(\mathrm{a}\right)$ initial velocity of the particle,
$\left(\mathrm{b}\right)$ angle between the position vector and velocity of the particle at any time, and
$\left(\mathrm{c}\right)$ speed at any instant.

A drag racer crosses the finish line, and the driver deploys a parachute and applies the brakes to slow down, as the figure illustrates. The driver begins slowing down when $t_1=10 \mathrm{s}$ and the car's velocity is ${\overrightarrow{v}}_1=+25 \mathrm{m} {\mathrm{s}}^{-1}.$ When $t_2=15 \mathrm{s},$ the velocity has been reduced to ${\overrightarrow{v}}_2=+15 \mathrm{m} {\mathrm{s}}^{-1}.$ What is the average acceleration of the dragster?

A particle describes an angle $\theta$ in a circular path with a constant speed $v.$ Find

(a) The change in the velocity of the particle.

(b) Average acceleration of the particle during the motion in the curve (circle).

A particle's position on the $x$ axis is given by $x=4-27t+t^3,$ with $x$ in meters and $t$ in seconds.

(a) Find the particle's velocity function $v\left(t\right)$ and acceleration function $a\left(t\right).$

(b) Is there ever a time when $v=0 ?$

(c) Describe the particle's motion for $t\ge 0.$

Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car $A$ exceeds that of car $B$. Does that mean that the acceleration of car $A$ is greater than that of car $B$? Explain.

Say Yes or No.

Can an object moving towards north have acceleration towards south?

Can a body have

Zero instantaneous velocity and yet be accelerating?