A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d. The average speed for this round trip is

The positions x of a particle with respect to time t along x-axis is given by x = 9t² $$-$$ t³ where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

$$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors and $$\theta $$ is the angle between them, if $$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \left( {\overrightarrow A .\overrightarrow B } \right),$$ the value of $$\theta $$ is

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) planes. Its coordinates at a later time are $$\left( {\sqrt 3 ,3} \right)$$. The path of the particle makes with the x-axes an angle of