Chapter 1
Kinematics (Motion)
Three Equations of Uniformly Accelerated Motion
SI: u, v in m/s; a in m/s²; t in s; s in m1) v = u + at | 2) s = ut + (1/2)at² | 3) v² = u² + 2as
These equations ONLY hold when acceleration a is constant in magnitude and direction.
Variables: u = initial velocity, v = final velocity, a = constant acceleration, t = time, s = displacement
Exam Tip: For body dropped from rest: u = 0, a = +g => v = gt, s = (1/2)gt², v² = 2gs.
Average Velocity & Speed
SI: m/sAverage Velocity = Total Displacement / Total Time | For constant acceleration: v_avg = (u + v) / 2
A body returning to its starting point has displacement = 0, so average velocity = 0, but distance and speed are non-zero.
Variables: Displacement is a vector quantity (can be 0 or negative); Distance is scalar (always ≥ 0).
Exam Tip: JEE Foundation: Harmonic mean formula for two equal distance legs with speeds v1 and v2: v_avg = 2v1v2 / (v1 + v2).
Chapter 2
Force & Laws of Motion
Newton Second Law & Momentum
SI: Newton (N) = kg·m/s²p = m × v | F = Δp / Δt = m(v - u) / t = m × a
The rate of change of momentum of an object is directly proportional to the applied unbalanced force.
Variables: p = linear momentum (kg·m/s), m = mass (kg), v = velocity (m/s), F = Force (N)
Exam Tip: Impulse = F × Δt = Δp (Change in momentum). Catching a cricket ball by pulling hands back increases Δt to reduce impact force F.
Law of Conservation of Linear Momentum
m1u1 + m2u2 = m1v1 + m2v2
In the absence of external unbalanced forces, the total momentum of an isolated system remains conserved.
Variables: m1, m2 = masses of colliding objects; u1, u2 = initial velocities; v1, v2 = final velocities
Exam Tip: Recoil velocity of gun: V_gun = -(m_bullet × v_bullet) / M_gun. The minus sign indicates opposite direction.