A man in a balloon rising vertically with an acceleration of $4.9\, m/sec^2$, releases a ball $2\, seconds$ after the balloon is let go from the ground. the greatest height above the ground reached by the ball is ..........$m$ :-

The displacement $x$ of a particle varies with time $t$ as $x = a{e^{ - \alpha t}} + b{e^{\beta t}}$ , where $a, b, \alpha$ and $\beta $ are positive constants. The velocity of the particle will

The displacement-time graph for two particles $A$ and $B$ are straight lines inclined at angles of $30^o$ and $60^o$ with the time axis. The ratio of velocities of $V_A : V_B$ is

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

Figure shows the graph of $x$-coordinate of a particle moving along $x$-axis as a function of time. Average velocity during $t=0$ to $6 \,s$ and instantaneous velocity at $t=3 \,s$ respectively, will be

Which of the following option is correct for a object having a straight line motion represented by the following graph ?