The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos$$\omega $$t
y = a sin$$\omega $$t and
z = a$$\omega $$t

The speed of the particle is :

A particle is moving with a velocity

$$\overrightarrow v \, = K(y\widehat i + x\widehat j),$$ where K is a constant.

The general equation for its path is :

A man in a car at location Q on a straight highway is moving with speed $$\upsilon $$. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?

A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ is along the ground and $${\widehat j}$$ is along the vertical. If g = 10 m/s², the equation of its trajectory is: