A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed $v (t)$ is depicted by which of the following curves?

A shell is fired vertically upwards with a velocity $v_1$ from a trolley moving horizontally with velocity $v_2$. A person on the ground observes the motion of the shell as a parabola, whose horizontal range is ....

A football player throws a ball with a velocity of $50$ metre/sec at an angle $30 $ degrees from the horizontal. The ball remains in the air for  ...... $\sec$ $(g = 10\,m/{s^2})$

From the top of a tower of height $40\,m$, a ball is projected upwards with a speed of $20\,m / s$ at an angle of elevation of $30^{\circ}$. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take $g=10\,m / s ^2$ )

The $x-t$ graph of a particle moving along a straight line is shown in figure The speed-time graph of the particle is correctly shown by

A cricket ball is thrown at a speed of $28\; m /s$ in a direction $30^o$ above the horizontal. Calculate

$(a)$ the maximum height,

$(b)$ the time taken by the ball to return to the same level, and

$(c)$ the distance from the thrower to the point where the ball returns to the same level