91Ó°ÊÓ

A parlicle moving along positive \(x\) -axis with a speed \(5 \mathrm{~ms}^{-1}\) suddenly changes its direction along the positive \(y\) -axis with the same speed. The change in velocity of the particle is: (a) \(-5(\hat{i}+\hat{j}) \mathrm{ms}^{1}\) (b) \(-5(\hat{i}-\hat{j}) \mathrm{ms}^{1}\) (c) \(-5 \sqrt{2}(\hat{i}+\hat{j}) \mathrm{ms}^{-1}\) (d) \(5 \sqrt{2}(\hat{i}+\hat{j}) \mathrm{ms}^{-1}\)

Statement-1: A body can have acceleration even if its velocity is zero at a given instant of time. Statement-2: A body is at rest when it reverses its direction of motion.

'Two particles start moving from the same point along the same straight line. The first moves with constant velocity \(v\) and the second with constant acceleration \(a\). During the time that elapses before the second catches the first, what is the greatest distance between the particles.

The position \(y\) of a particle depends on time as \(y=A \sin (\omega t+\varphi)\), where \(A, \omega\) and \(\varphi\) is a \((+v e)\) constant. At \(t=0\), the particle is at \(y-\frac{A}{2}\). Find \(\left(\frac{d^{2} y}{d t^{2}}\right)\) at \(t-\left(\frac{\pi}{\omega}\right) \mathrm{sec}\). (a) \(\frac{\omega^{2} A}{2}\) (b) \(\omega^{2} A\) (c) \(\frac{\omega^{2} A \sqrt{3}}{2}\) (d) zero