$A$ body has speeds $V$,$2V$,and $3V$ in the first $1/3$ of distance $S$,the second $1/3$ of distance $S$,and the third $1/3$ of distance $S$ respectively. Its average speed will be:

$A$ 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 $m/s$)

$A$ particle moving in a straight line covers half the distance with a speed of $3 \, m/s$. The other half of the distance is covered in two equal time intervals with speeds of $4.5 \, m/s$ and $7.5 \, m/s$ respectively. The average speed of the particle during this motion is...... $\, m/s$

"The magnitude of average velocity is equal to average speed". This statement is not always correct and not always incorrect. Explain with an example.

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 $m/s^2$)