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......$m/sec^2$
$-4$
$-5$
$-8$
$0$
An aircraft is flying at a height of $3400\; m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0\; s$ apart is $30^o$, what is the speed in $m/s$ of the aircraft ?
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are $(0,2)$. The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y =5 x (1- x )$. The $y$ component vector of the initial velocity is.
(Take $g=10\,m / s ^{2}$ )
A man moves in an open field such that after moving $10 \,m$ on a straight line, he makes a sharp turn of $60^{\circ}$ to his left. The total displacement just at the start of $8^{\text {th }}$ turn is equal to ........$m$
$List I$ describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. $List II$ gives possible magnitudes of then relative velocities (in $ms ^{-1}$ ) at time $t=\frac{\pi}{3} s$.
Which one of the following options is correct?