$Y $ component of velocity is $20$ and $X$ component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is

A particle has initial velocity of $\left( {\widehat i + \widehat j} \right)\, m/s$ and an acceleration of $\left( {\widehat i + \widehat j} \right)\, m/s^2$. Its speed after $10s$ will be :-

A horizontal plane supports a stationary vertical cylinder of radius $R = 1\ m$ and a disc $A$ attached to the cylinder by a horizontal thread $AB$ of length $l_0 = 2\ m$ (seen in figure, top view). An intial velocity ($v_0 = 1\ m/s$) is imparted $AB$ to the disc as shown in figure. .......... $\sec$ long will it move along the plane until it strikes against the cylinder ? (All surface are assumed to be smooth)

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

In the picture shown, a ball standing from rest rolls down a ramp $AB$, goes along at the horizontal bottom $BC$, and then backs up a smaller ramp $CD$, thereafter rolls on horizontal plane $DE$. Ignore friction and air resistance.Which of the following figure shows variation in speed with time ?

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