Kinematics is the branch of mechanics that describes the motion of objects without considering the forces causing the motion. It covers displacement, velocity, acceleration, and their relationships (NCERT Class 11 Chapter 3 & 4).
Equations of Motion (for uniform acceleration a, initial velocity u, final velocity v, time t, displacement s):
v = u + at – relates final velocity, initial velocity, acceleration, time
s = ut + ½at² – displacement in time t
v² = u² + 2as – velocity-displacement relation
s_n = u + a(2n-1)/2 – displacement in nth second
Projectile Motion is a 2D motion under gravity alone. Horizontal velocity (u = u·cos?) remains constant; vertical velocity (u = u·sin?) changes due to gravity. Range R = u²sin2?/g. Maximum height H = u²sin²?/2g. Time of flight T = 2u·sin?/g.
Velocity-Time Graph: The slope of a v-t graph gives acceleration; the area under the curve gives displacement. For uniform acceleration, the v-t graph is a straight line.
Projectile Motion Key Formulas
Quantity
Formula
Range (R)
R = u²sin2 / g
Max Height (H)
H = u²sin² / 2g
Time of Flight (T)
T = 2u·sin / g
Max range angle
= 45°
CBSE/NEET Tip: For maximum range on level ground, the angle of projection is 45°. At 45°, sin2 = sin90° = 1 (maximum). Two angles giving same range are complementary: and (90°-?).