$A$ ball is thrown vertically upwards. Which of the following graphs represents the velocity-time graph of the ball during its flight (air resistance is neglected)?

Fill in the blanks:
$(a)$ The path length is always ............ .
$(b)$ The slope of the velocity-time graph for an object moving with acceleration is ............ .
$(c)$ If the velocity-time graph is parallel to the time-axis,the object is ............ .

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?

Two cars $A$ and $B$ start from a point at the same time in a straight line and their positions are represented by $R_{A}(t) = at + bt^2$ and $R_{B}(t) = xt - t^2$. At what time do the cars have the same velocity?

The displacement $x$ versus time graph is shown below. Analyze the following statements:
$(A)$ The average velocity during $0$ to $3\ s$ is $10\ m/s$.
$(B)$ The average velocity during $3$ to $5\ s$ is $0\ m/s$.
$(C)$ The instantaneous velocity at $t = 2\ s$ is $5\ m/s$.
$(D)$ The average velocity during $5$ to $7\ s$ and instantaneous velocity at $t = 6.5\ s$ are equal.
$(E)$ The average velocity from $t = 0$ to $t = 9\ s$ is zero.
Choose the correct answer from the options given below.