A particle comes round a circle of radius $1 \,m$ once. The time taken by it is $10 \,sec$. The average velocity of motion is

A particle is moving on a circular path of radius $r$ with uniform speed $v$. The magnitude of change in velocity when the particle moves from $P$ to $Q$ is  $(\angle POQ = 40^o)$

A particle moves in a circular path with decreasing speed. Choose the correct statement.

A particle moves so that its position vector is given by $\overrightarrow {\;r} = cos\omega t\,\hat x + sin\omega t\,\hat y$ , where $\omega$ is a constant.  Which of the following is true?  

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is

Three particle $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi }\,m$, in anticlockwise direction with speeds $1\, m/s$, $2. 5\, m/s$ and $2\, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in figure. The ratio of distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time is