$A$ particle moves towards east with velocity $5\, m/s$. After $10\, s$,its direction changes towards north with the same velocity. The average acceleration of the particle is

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option:

$A$ particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec{a} = (4\hat{i} + 3\hat{j}) \, m/s^2$ and $\vec{P} = (8\hat{i} - 6\hat{j}) \, kg \cdot m/s$. The motion of the particle is:

$A$ scooter going due east at $10\, ms^{-1}$ turns right through an angle of $90^\circ$. If the speed of the scooter remains unchanged in taking the turn,the change in the velocity of the scooter is

As shown in the figure,there is a spring-block system. $A$ block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring by $5.0\,cm$. The spring constant is $500\,N/m$. When released,calculate the horizontal distance from the edge of the table where it will hit the ground $4\,m$ below the spring. $(g = 10\,m/s^2)$

Two stones are projected so as to reach the same horizontal range on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the heights attained by them. Then,the angle of projection of the stone which attains the smaller height is $........$