A particle moves from the point $\left( {2.0\hat i + 4.0\hat j} \right)\,m$, at $t = 0$ with an initial velocity $\left( {5.0\hat i + 4.0\hat j} \right)\,m{s^{ - 1  }}$. It is acted upon by a constant force which produces a constant acceleration $\left( {4.0\hat i + 4.0\hat j} \right)\,m{s^{ - 2}}$. What is the distance of the particle from the origin at time $2\,s$

Ship $A$ is sailing towards north -east with velocity $\vec v = 30\,\hat i + 50\hat j\,km/hr$ where $\hat i$ points east and $\hat j$ , north. Ship $B$ is at a distance of $80\, km$ east and $150\, km$ north of Ship $A$ and is sailing towards west at $10\, km/hr$. $A$ will be at minimum distance from $B$ is.........$hrs$

A particle moves in the $xy$ -plane with velocity $u_x = 8t -2$ and $u_y = 2$. If it passes through  the point $(14, 4)$ at $t = 2\, s$, the equation of its path is 

A body of mass $1 \,\, kg$ is acted upon by a force $\vec F = 2\sin 3\pi t\,\hat i + 3\cos 3\pi t\,\hat j$ find its position at $t = 1 \,\, sec$ if at $t = 0$ it is at rest at origin. 

Find the value of Relative velocity of any two particles moving in a frame of reference.

What can be the angle between velocity and acceleration for the motion on a straight line ? Explain with example.