A person sitting in a moving train with his face towards the engine, throws a coin vertically upwards. The coin falls ahead of person. The train:

$Assertion$ : A body with constant acceleration always moves along a straight line.

$Reason$ : A body with constant acceleration may not speed up.

The velocity-displacement graph of a particle is shown in the figure.

The acceleration-displacement graph of the same particle is represented by :

The position$(x)$ of a particle at any time$(t)$ is given by $x(t) = 4t^3 -3t^2 + 2$ The acceleration and velocity of the particle at any time $t = 2\, sec$ are respectively

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x -$ axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration, $v =$ velocity, $x =$ displacement, $t =$ time)

The displacement $(x)$ of a particle depends on time $t$ as $x=\alpha t^2-\beta t^3$. Choose the incorrect statements from the following.