What is the acceleration of the particle on $OA$,$AB$,and $BC$ respectively?

The $x-t$ graph for a uniformly accelerated particle is as shown in the figure. Find the average velocity between points $(i)$ and $(ii)$ in $ms^{-1}$.

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha, \text{and } \beta$ are positive constants. The velocity of the particle will:

From the velocity-time graph of a particle moving in a straight line,decide which of the following is an incorrect statement.

The given graph shows the variation of velocity $(v)$ with position $(x)$ for a particle moving along a straight line. Which of the following graphs shows the variation of acceleration $(a)$ with position $(x)$?

What is common in the two graphs given below?