In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t=x^2+x$. The acceleration of the particle is

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. A girl is driving scooty with a speed of $60 \mathrm{~km} / \mathrm{h}$ in the direction $X$ to $Y$ notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.

A particle is moving along $$x$$-axis with its position (x) varying with time $$(t)$$ as $$x=\alpha t^4+\beta t^2+\gamma t+\delta$$. The ratio of its initial velocity to its initial acceleration, respectively, is:

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 :