Mark the correct statements for a particle moving in a straight line.

State whether the following statements are true or false:
$(a)$ An object can have acceleration even when its velocity is zero.
$(b)$ If the acceleration of a moving object is constant,the direction of its velocity must remain the same.
$(c)$ The speed of an object can never be zero.

$A$ bogie of a uniformly moving train is suddenly detached from the train and stops after covering some distance. What is the relation between the distance covered by the bogie and the distance covered by the train in the same time?

$A$ car moves in the positive $Y$-direction with velocity $v$ proportional to the distance travelled $y$ as $v(y) \propto y^\beta$, where $\beta$ is a positive constant. The car covers a distance $L$ with average velocity $\langle v \rangle$ proportional to $L$ as $\langle v \rangle \propto L^{1/3}$. The constant $\beta$ is given as:

$A$ 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.

Let $v$ and $a$ denote the velocity and acceleration respectively of a body. Which of the following statements is correct?