$A$ particle is moving along the $Y$-axis. The position of the particle from the origin as a function of time $(t)$ is given as $y(t) = 10 t e^{-2 t}$. How far is the particle from the origin when it stops momentarily? ($y$ is given in units of metre and $t$ is in units of second)

Two small blocks slide without losing contact with the surface along two frictionless tracks $1$ and $2$,starting at the same time with the same initial speed $v$. Track $1$ is perfectly horizontal,while track $2$ has a dip in the middle,as shown in the figure. Which block reaches the finish line first? [Hint: Use velocity-time graph to solve]

The acceleration-time graph of a body is shown below. The most probable velocity-time graph of the body is:

$A$ train starting from rest travels the first part of its journey with constant acceleration $a$,the second part with constant velocity $v$,and the third part with constant retardation $a$,finally being brought to rest. The average speed for the whole journey is $\frac{7v}{8}$. The train travels with constant velocity for what fraction of the total time?

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

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance (in $m$) covered by the object between $t = 0$ and $t = 4 \; s$?