A particle has initial velocity $\left( {2\hat i + 3\hat j} \right)$ and acceleration $\left( {0.3\hat i + 0.2\hat j} \right)$. The magnitude of velocity after $10\, seconds$ will be
$5\, units$
$9\, units$
$9\sqrt 2 \,unit$
$5\sqrt 2 \,unit$
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 position vector of a particle $\vec R$ as a function of time is given by $\overrightarrow {\;R} = 4\sin \left( {2\pi t} \right)\hat i + 4\cos \left( {2\pi t} \right)\hat j$ where $R$ is in meters, $t$ is in seconds and $\hat i$ and $\hat j$ denote unit vectors along $x-$ and $y-$directions, respectively. Which one of the following statements is wrong for the motion of particle?
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 $(g = 10\, m/s^2)$
Velocity of a particle moving in a curvilinear path in a horizontal $X$ $Y$ plane varies with time as $\vec v = (2t\hat i + t^2 \hat j) \ \ m/s.$ Here, $t$ is in second. At $t = 1\ s$