If the position-time graph of a particle is a sine curve as shown,what will be its velocity-time graph?

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?

The distance travelled by a particle is related to time $t$ as $x = 4t^2$. The velocity of the particle at $t = 5 \, s$ is $......... \, ms^{-1}$.

The maximum possible acceleration of a train moving on a straight track is $10\ m/s^2$ and the maximum possible retardation is $5\ m/s^2$. If the maximum achievable speed of the train is $10\ m/s$,then the minimum time in which the train can complete a journey of $135\ m$ starting from rest and ending at rest is.........$s$.

The displacement-time graph for two particles $A$ and $B$ is as follows. The ratio $\frac{v_A}{v_B}$ is

The diagram shows the variation of $1/v$ (where $v$ is the velocity of the particle) with respect to time $t$. Using the details given in the graph,the instantaneous acceleration at time $t = 3\,s$ will be equal to $...........\,m/s^2$.