A particle moves along an arc of a circle of radius $R$ . Its velocity depends on the distance covered as $v = a\sqrt s$ , where $a$ is a constant then the angle $\alpha $ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be
$\tan \alpha = \frac{R}{{2s}}$
$\tan \alpha = \frac{2s}{{R}}$
$\tan \alpha = \frac{2R}{{s}}$
$\tan \alpha = \frac{s}{{2R}}$
A particle has initial velocity $(2\hat i + 3\hat j ) $ and has acceleration $(0.3\,\hat i + 0.2\,\hat j)$ . Its speed after $10\,s$ is
The coordinates of a moving particle at any time are given by $x = a{t^2}$ and $y = b{t^2}$. The speed of the particle at any moment is
A particle moves in space along the path $z = ax^3 + by^2$ in such a way that $\frac{dx}{dt} = c = \frac{dy}{dt}.$ Where $a, b$ and $c$ are contants. The acceleration of the particle is
Two particles are projected simultaneously in the same vertical plane, from the same point on ground, but with same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one, as seen by the other, is