The velocity of a particle is given by the equation $v(x) = 3x^2 - 4x$,where $x$ is the distance covered by the particle. The expression for its acceleration is

The position, velocity, and acceleration of a particle moving with a constant acceleration can be represented by which of the following sets of graphs?

What is retardation?

The velocity $(v)-$ time $(t)$ plot of the motion of a body is shown below:
The acceleration $(a)-$ time $(t)$ graph that best suits this motion is:

$A$ particle is moving in one dimension (along $x$-axis) under the action of a variable force. Its initial position was $16 \,m$ right of the origin. The variation of its position $(x)$ with time $(t)$ is given as $x = -3t^3 + 18t^2 + 16t$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the particle when its acceleration becomes zero is . . . . . . $m/s$.

The correct position $(x)$ - time $(t)$ graph for a particle moving with negative acceleration is