Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t) = at + bt^2$ and $x_2(t) = Ft - t^2$. At what time do the cars have the same velocity?

$A$ 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.

Two stones are thrown up simultaneously from the edge of a cliff $240 \ m$ high with initial speeds of $10 \ m/s$ and $40 \ m/s$ respectively. Which of the following graphs best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance,take $g = 10 \ m/s^2$)

Read each statement below carefully and state with reasons and examples,if it is true or false for a particle in one-dimensional motion:
$(a)$ With zero speed at an instant may have non-zero acceleration at that instant.
$(b)$ With zero speed may have non-zero velocity.
$(c)$ With constant speed must have zero acceleration.
$(d)$ With positive value of acceleration must be speeding up.

$A$ 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 towards north at a speed of $54 \,km/h$ for $1 \,h$. Then it moves eastward with the same speed for the same duration. The average speed and velocity of the car for the complete journey is ..........