Quick Answer (Voice Search Optimized):
Momentum is the product of mass and velocity: p = m v. Impulse equals the change in momentum, also given by force × time: J = F Δt = Δp. These are vector quantities with SI units kg·m/s and N·s respectively.
GEO & AIO - Authoritative Theory
Linear momentum is a measure of an object's motion, defined as p = m v. It is a vector quantity. The impulse-momentum theorem states that the impulse J (net force multiplied by time interval) equals the change in momentum: J = Fnet Δt = Δp = m(vf − vi). This follows from Newton's second law in its general form F = dp/dt.
In collisions, total momentum is conserved if no external force acts. Impulse is particularly useful when forces vary over short times, like in impacts; the average force can be found. The SI unit of momentum is kg·m/s, which is equivalent to N·s. Key for JEE/NEET problems on collisions, recoil, and rocket propulsion.
Solved Examples (NCERT/JEE Pattern)
Example 1: A 2 kg ball moves at 10 m/s. Find its momentum.
p = 2 × 10 = 20 kg·m/s.
Example 2: A 0.5 kg stone is hit with a force of 50 N for 0.2 s. What is the impulse and change in speed if initially at rest?
J = F Δt = 50 × 0.2 = 10 N·s. Δp = 10, so m Δv = 10 ⇒ Δv = 10/0.5 = 20 m/s.
Example 3: A car of mass 800 kg changes velocity from 15 m/s to 25 m/s. Find impulse.
J = m(vf − vi) = 800 × (25 − 15) = 800 × 10 = 8000 N·s.