Figure shows a body of mass m moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is

A particle moves along an arc of a circle of radius $R$ . Its velocity depends on the distance covered as $v = a\sqrt s$ , where $a$ is a constant then the angle $\alpha $ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be

The graph of position $x$ versus time $t$ represents the motion of a particle. If $b$ and $c$ are both positive constants, which of the following expressions best describes the acceleration $a$ of the particle?

A vector has magnitude and direction. Does it have a location in space ? Can it vary with time ? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.

A particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is