An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

A solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \mathrm{~m} / \mathrm{s}$ at the bottom of the inclination. How far will the ball go up the plane?

(Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A particle performs simple harmonic motion with a time period of 16 s . At a time $t=2 \mathrm{~s}$, the particle passes through the origin and at $t=4 \mathrm{~s}$ its velocity is $4 \mathrm{~m} / \mathrm{s}$. The amplitude of the motion is

Let the escape speed of an object on the earth's surface be $v_0$. The object is projected out with speed $5 v_0$. The speed of the object far away from the earth will be