What is acceleration? What is its direction,and state its $SI$ unit.

When are the average and instantaneous accelerations equal?

$Assertion$ : Retardation is directly opposite to the velocity.
$Reason$ : Retardation is equal to the time rate of decrease of speed.

The graph of position $x$ versus time $t$ represents the motion of a particle. The curve is a parabola opening upwards. If the equation of motion is given by $x = a + bt - ct^2$ where $b$ and $c$ are positive constants,which of the following expressions best describes the acceleration $a_{acc}$ of the particle?

The position $x$ of a particle varies with time as $x = at^2 - bt^3$,where $a$ and $b$ are constants. The acceleration of the particle will be zero at:

The velocity of a particle is given as $\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k} \text{ m/s}$. The magnitude of acceleration at point $(1, 2, 4)$ is . . . . . . $\text{m/s}^2$.