$A$ car moves from $X$ to $Y$ with a uniform speed $v_1$ and returns from $Y$ to $X$ with a uniform speed $v_2$. The average speed for this round trip is

$A$ body travelling along a straight line path travels the first half of the distance with a velocity of $7 \,m/s$. During the travel time of the second half of the distance, the first half of the time is travelled with a velocity of $14 \,m/s$ and the second half of the time is travelled with a velocity of $21 \,m/s$. Then the average velocity of the body during the entire journey is: (in $\,m/s$)

The ratio of the numerical values of the average velocity and average speed of a body is always

The position of an object moving along the $X$-axis is given by $x = \alpha + \beta t^2$, where $\alpha$ and $\beta$ are constants with appropriate dimensions and $t$ is time in seconds. The average velocity between $t = 2 \ s$ and $t = 4 \ s$ is $12 \ m/s$. If $\alpha = 8 \ m$, then the value of $\beta$ is: (in $m/s^2$)

$A$ person travels along a straight road for half the distance with velocity $v_1$ and the remaining half distance with velocity $v_2$. The average velocity is given by:

$A$ particle travels half of the distance of a straight journey with a speed $6 \,m/s$. The remaining part of the distance is covered with speed $2 \,m/s$ for half of the time of the remaining journey and with speed $4 \,m/s$ for the other half of the time. The average speed of the particle is ....... $m/s$.