A particle moves in a straight line and its position $x$ at time $t$ is given by $x^2=2+t$. Its acceleration is given by

Given figure shows the $x-t$ plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for $t < 0$ and on a parabolic path for $t >0$? If not, suggest a suitable physical context for this graph.

Velocity-displacement graph of a particle moving in a straight line is as shown in figure

A particle of unit mass undergoes one­ dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ – 2n}}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

The distance-time graph of a particle at time $t$ makes angle $45^{\circ}$ with the time axis. After one second, it makes angle $60^{\circ}$ with the time axis. What is the average acceleration of the particle?