The acceleration-time graph for a body is shown in the graph. Which of the following  graphs would probably represent velocity of the body plotted against time:-

Which of the following statements are true for a moving body?

The velocity of a body depends on time according to the equation $v = 20 + 0.1{t^2}$. The body is undergoing

A ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).

$(a)$ Plot qualitatively velocity versus time graph.

$(b)$ Plot qualitatively acceleration versus time graph.

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 travelled by a body moving along a line in time $t$ is proportional to $t^3$. The acceleration-time $(a, t)$ graph for the motion of the body will be