A particle undergoes three successive displacements given by $s _1=\sqrt{2}\,m$ north-east, $s _2=2\,m$ due south and $s _3=4\,m , 30^{\circ}$ north of west, then magnitude of net displacement is

The figure shows a velocity-time graph of a particle moving along a straight line  The correct displacement-time graph of the particle is shown as

The $x$ and $y$ coordinates of the particle at any time are $x = 5t - 2t^2$ and $y = 10t$ respectively, where $x$ and $y$ are in metres and $t$ in seconds. The acceleration of the particle at $t = 2\, s$ is......$m/sec^2$

A particle is moving along the $x-$axis with its coordinate with the time '$t$' given be $\mathrm{x}(\mathrm{t})=10+8 \mathrm{t}-3 \mathrm{t}^{2} .$ Another particle is moving the $y-$axis with its coordinate as a function of time given by $\mathrm{y}(\mathrm{t})=5-8 \mathrm{t}^{3} .$ At $\mathrm{t}=1\; \mathrm{s},$ the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{\mathrm{v}} .$ Then $\mathrm{v}$ (in $\mathrm{m} / \mathrm{s})$ is

Two stones are thrown up vertically and simultaneously but with different speeds. Which graph correctly represents the time variation of their relative positions $\Delta x$.Assume that stones do not bounce after hitting ground.

An observer moves with a constant speed along the line joining two stationary objects. He will observe that the two objects