$A$ particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2$. Its average speed during the complete journey is

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 $m/s^2$)

The position of an object moving along the $x$-axis is given by $x = a + b t^2$,where $a = 8.5 \; m$,$b = 2.5 \; m s^{-2}$,and $t$ is measured in seconds. What is the average velocity between $t = 2.0 \; s$ and $t = 4.0 \; s$ (in $; m s^{-1}$)?

$A$ person walks along a straight road from his house to a market $2.5 \,km$ away with a speed of $5 \,km/h$ and instantly turns back and reaches his house with a speed of $7.5 \,km/h$. The average speed of the person during the time interval $0$ to $50 \,min$ is (in $m/s$)

$A$ 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: