Motion of a particle in $x – y$ plane is described by a set of following equations $x=4 \sin \left(\frac{\pi}{2}-\omega t\right) m$ and $y=4 \sin (\omega t) m$. The path of particle will be 

When the average and instantaneous accelerations are equal ?

The length of second's hand in watch is $1 \,cm.$ The change in velocity of its tip in $15$ seconds is

The position vector of a particle changes with time according to the relation $\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 – 20{t^2}} \right)\hat j$. What is the magnitude of the acceleration at $t = 1$ ?

The figure shows the velocity and the acceleration of a point like body at the initial moment of its motion. The direction and the absolute value of the acceleration remain constant. Find the time when the speed becomes minimum………$s$ (Given : $a = 4\, m/s^2, v_0 = 40\, m/s, \phi =143^o$)