A projectile is projected with speed $u$ at an angle $\theta$ with the horizontal. The average velocity of the projectile between the instants it crosses the same level is ............
$u \cos \theta$
$u \sin \theta$
$u \cot \theta$
$u \tan \theta$
A particle starts moving rectilinearly at time $t = 0$ such that its velocity $'v'$ changes with time $'t'$ according to the equation $v = t^2 - t$ where $t$ is in seconds and $v$ is in $m/s.$ The time interval for which the particle retards is
The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5{t^2})$ meter and $x = 6t\, meter$, where $t$ is in second. the angle with the horizontal at which the projectile was projected is
A body throws a ball upwards with velocity $v_0 = 20\, m/s$ . The wind imparts a horizontal acceleration of $4\, m/s^2$ to the ball. The angle $\theta $ from vertical at which the ball must be thrown so that the ball returns to the boy's hand is $(g = 10\, m/s^2)$
A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a = (4\hat i + 3\hat j)\ m/s^2$ and $\vec p = (8\hat i - 6\hat j)\ kg-m/s$ . The motion of the particle is
Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc, the distance through which $P$ moves in one full rotation of the disc is