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 ..........  $km$. $(g = 10\,\,m/{s^2})$

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 

A point $P$ moves in counter clock wise direction on a circular path as shown in figure.  The movement of $'P'$ is such that it sweeps out a length $S = t^3 + 5$, where $'S'$ is in meter and $t$ is in seconds. The radius of the path is $20\, m$. The acceleration of $'P'$ when $t = 2\, sec$. is nearly     ......... $m/s^2$

Two cars of masses $m_1$ & $m_2$ are moving along the circular paths of radius $r_1$ & $r_2$ respectively. Their speeds are such that they complete one round in same time. The ratio of angular speeds of two cars is

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

A particle has initial velocity $(3\hat i + 4\hat j$$ ) $ and has acceleration $(0.4\,\hat i + 0.3\,\hat j)$ . Its speed after $10\,s$ is