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

Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to horizontal, after one more second it is travelling horizontally. What is the magnitude and direction of its velocity at initial point 

An aircraft executes a horizontal loop with a speed of $150 \,m/s$ with its, wings banked at an angle of ${12^o }$. The radius of the loop is ..........  $km$. $(g = 10\,\,m/{s^2})$

A particle is moving on a circular path of radius $r$ with uniform velocity $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = {40^o})$

ball is thrown from a point with a speed $‘v_0$’ at an elevation angle of $\theta $ . From the same point and at the same instant, a person starts running with a constant speed $\frac{{'{v_0}'}}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection $\theta $ ?

If the instantaneous velocity of a particle projected as shown in figure is given by $v =a \hat{ i }+(b-c t) \hat{ j }$, where $a, b$, and $c$ are positive constants, the range on the horizontal plane will be