The position of a particle moving in the $xy-$ plane at any time $t$ is given by $x = (3t^2 -6t)\, metres$, $y = (t^2 -2t)\,metres$. Select the correct statement about the moving particle from the following
The acceleration of the particle is zero at $t = 0\, second$
The velocity of the particle is zero at $t = 0\, second$
The velocity of the particle is zero at $t = 1\, second$
The velocity and acceleration of the particle are never zero
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 ball is rolled off along the edge of a horizontal table with velocity $4 m/s$. It hits the ground after time $0.4 \,\,s$. Which of the following are correct?
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 changes with time according to the relation $\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 - 20{t^2}} \right)\hat j$. What is the magnitude of the acceleration at $t = 1$ ?