From a tower of height $H$, a particle is thrown vertically
upwards with a speed $u$. The time taken by the particle to hit
the ground, is $n$ times that taken by it to reach the highest point
of its path. The relation between $H, u$ and $n$ is
Time taken to reach highest point is $t_{1}=\frac{u}{g}$ Speed on reaching ground $=\sqrt{u^{2}+2gh}$ Now, $v=u+at$ $\Rightarrow \sqrt{u^{2}+2 g h}=-u+gt$ $\Rightarrow t=\frac{u+\sqrt{u^{2}+2 g H}}{g}=\frac{nu}{g}$ $\Rightarrow 2gH=n(n-2) u^{2}$
The motion in a straight lineis an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.
