A vehicle travels half the distance with speed $v$ and the remaining distance with speed $2\,v$.Its average speed is :

A person travels $x$ distance with velocity $v_1$ and then $x$ distance with velocity $v_2$ in the same direction. The average velocity of the person is $v$, then the relation between $v , v _1$ and $v _2$ will be :

A horse rider covers half the distance with $5\,m / s$ speed. The remaining part of the distance was travelled with speed $10\,m / s$ for half the time and with speed $15 m / s$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7}\,m / s$. The value of $x$ is

A person goes from point $P$ to point $Q$ covering $1 / 3$ of the distance with speed $10 \,km / h$, the next $1 / 3$ of the distance at $20 \,km / h$ and the last $1 / 3$ of the distance at $60 \,km / h$. The average speed of the person is ............ $km / h$

A cyclist starts from the centre $O$ of a circular park of radius one kilometre, reaches the edge $P$ of the partk. Then cycles along the circumference and returns to the centre along $QO$ as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour respectively) is

A point traversed $3 / 4$ th of the circle of radius $R$ in time $t$. The magnitude of the average velocity of the particle in this time interval is