The initial velocity of a projectile is $\vec{u} = (4\hat{i} + 3\hat{j})\,m/s$. It is moving with uniform acceleration $\vec{a} = (0.4\hat{i} + 0.3\hat{j})\,m/s^2$. The magnitude of its velocity after $10\,s$ is.........$m/s$.

$A$ ball of mass $100 \ g$ is projected with velocity $20 \ m/s$ at $60^{\circ}$ with the horizontal. The decrease in kinetic energy of the ball during the motion from the point of projection to the highest point is:

In the following cases,identify the source providing the centripetal force:
$(i)$ Motion of the Earth around the Sun.
$(ii)$ Motion of an electron around the nucleus.
$(iii)$ Motion of a vehicle on a horizontal curved road.

$A$ particle of mass $m$ performs uniform circular motion of radius $r$ with linear speed $v$ under the application of force $F$. If $m, v$ and $r$ are all increased by $50 \%$,the necessary change in force required to maintain the particle in uniform circular motion is (in $\%$)

$A$ particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. At point $(0, b)$,the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

$A$ particle moves around a circular path of radius $r$ with uniform speed $V$. After moving half the circle,the average acceleration of the particle is