A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \,s$ ?
The position vector of an object at any time $t$ is given by $3 t^2 \hat{i}+6 t \hat{j}+\hat{k}$. Its velocity along $y$-axis has the magnitude
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 $(g = 10\, m/s^2)$
What can be the angle between velocity and acceleration for the motion on a straight line ? Explain with example.