The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance traversed by the particle in $m$ between $t=2\;s$ to $6\;s$.

In the picture shown,a ball starting from rest rolls down a ramp $AB$,moves along the horizontal bottom $BC$,then goes up a smaller ramp $CD$,and thereafter rolls on the horizontal plane $DE$. Ignore friction and air resistance. Which of the following figures shows the variation in speed with time?

What is the acceleration of the particle on $OA$,$AB$,and $BC$ respectively?

The position $x$ of a particle at any time $t$ is given by $x(t) = 4t^3 - 3t^2 + 2$. The acceleration and velocity of the particle at $t = 2 \, s$ are respectively:

In the following displacement $x$ versus time $t$ graph,at which among the points $P, Q$ and $R$ is the object's speed increasing?

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?