G L Mittal and TARUN MITTAL Solutions for Chapter: Motion in One and Two Dimensions, Exercise 1: QUESTIONS

Show that the area enclosed by time-acceleration graph and time-axis of an object for a certain interval of time is equal to the velocity-change for that time-interval.

Derive the following relation either graphically or mathematically:

$v=u+at$

Derive the following relation either graphically or mathematically:

$s=ut+\frac{1}{2}a{t}^2$

Derive the following relation either graphically or mathematically:

$v^2=u^2+2as$

If a projectile is projected at an angle $\theta$ from the horizontal with velocity $u$ in the gravitational field, prove that the path of the projectile will be a parabola.
Can path of projectile be rectilinear?
 

If $h$ be the maximum height of a projectile moving under the gravitational field of earth, then prove that its velocity of projection will be
$\frac{\sqrt{2gh}}{\sin \theta }$, where $\theta$ is the angle of projection.
 

A projectile is thrown at an angle $\theta$ from the horizontal with velocity $u$ under the gravitational field of the earth. Find its time of flight, maximum height attained and the range.

Show that the horizontal range of a projectile with initial speed $u$ and angle of projection $\theta$ is $\frac{u^2\sin 2\theta }{g}$ .  At what angle of projection is the horizontal range maximum for a given initial speed of the projectile? What is this maximum range?