Suggest a suitable physical situation for following graphs.
In the given $v$ -t graph, the sign of velocity changes and its magnitude decreases with a passage of time. A similar situation arises when a ball is dropped on the hard floor from a height. It strikes the floor with some velocity and upon rebound, its velocity decreases by a factor. This continues till the velocity of the ball eventually becomes zero.
The acceleration (a)-time $(t)$ graph for a particle moving along a straight starting from rest is shown in figure. Which of the following graph is the best representation of variation of its velocity $(v)$ with time $(t)$ ?
The displacement $(x)$ of a particle depends on time $t$ as $x=\alpha t^2-\beta t^3$. Choose the incorrect statements from the following.
For a moving body at any instant of time
The initial velocity of a particle is $u\left(\right.$ at $t=0$ ) and the acceleration a is given by $\alpha t^{3 / 2}$. Which of the following relations is valid?