A particle is projected from the origin with speed V m/s at an angle a to the norizontal. 4 a Assuming that the coordinates of the particle at time t are (Vt cos a, Vt sin a – gt2), prove that the horizontal range R of the particle v² sin 2a is *(1 - Jun 6 b Hence prove that the path of the particle has equation y = x tan a. R c Suppose that a = 45° and that the particle passes through two points 6 metres apart and 4 metres above the point of projection, as shown in the diagram. Let x-coordinates of the two points. and x2 be the i Show that x1 and x2 are the roots of the equation x2 ii Use the identity (x2 - x1)? = (x2 + x1) - 4xx¡ to find R. Rx + 4R = 0.

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, fo…