$A$ particle moving in a straight line covers half the distance with speed $6 \, m/s$. The other half is covered in two equal time intervals with speeds $9 \, m/s$ and $15 \, m/s$ respectively. The average speed of the particle during the motion is: (in $ \, m/s$)

The $v-t$ graph of an object of mass $1\,\text{kg}$ is shown. Which of the following statements is correct?

$A$ particle moves along a straight line such that its displacement $x$ varies with time $t$ as $x = \alpha t^3 + \beta t^2 + \gamma$, where $\alpha, \beta, \gamma$ are constants. $V_1$ is the average velocity of the particle during its journey between $t = 1 \ s$ and $t = 3 \ s$. $V_2$ is the instantaneous velocity of the particle at $t = 3 \ s$. The ratio $\frac{V_1}{V_2}$ is

Assertion $(A)$: The angle between acceleration and velocity of a body in one-dimensional motion is always zero. Reason $(R)$: One-dimensional motion is along a straight line.

$A$ particle has an initial velocity of $10 \, m/s$. It moves due to a constant retarding force along the line of motion,which produces a retardation of $5 \, m/s^2$. Then:

$A$ car travels from $A$ to $B$ (without changing direction). During the first part of the journey,its average speed is $V_1$,and for the second part of the journey,its average speed is $V_2$. The ratio of the path length of the second part to the path length of the first part is $\sqrt{\frac{V_2}{V_1}}$. In this case,the average speed of the total path is the ....... of the average speeds of both parts. Choose the correct option.