(a)(i) Define the term linear momentum. (ii) State the law of conservation of linear momentum. (b) A ball P of mass 0.25 kg, loses one-third of its velocity...

(a)(i) Linear momentum is the product of the mass of a body and its velocity, \(p = mv\). It is a vector quantity with SI unit \(\text{kg m s}^{-1}\).

(a)(ii) Law of conservation of linear momentum: In a closed system on which no external resultant force acts, the total linear momentum before an interaction (e.g. a collision) equals the total linear momentum after it.

(b) Let the initial velocity of P be \(u\). Both balls have equal mass \(m = 0.25\ \text{kg}\). P loses one-third of its velocity, so after collision P moves with \(v_P = u - \tfrac{1}{3}u = \tfrac{2}{3}u\). Q starts at rest and moves off at \(v_Q = 2\ \text{m s}^{-1}\).

Conservation of momentum (mass cancels):

Initial velocity of P \(= 6\ \text{m s}^{-1}\).

(c)(i) Newton's second law: The rate of change of momentum of a body is directly proportional to the resultant force acting on it and takes place in the direction of that force.

(c)(ii) For a body of mass \(m\) whose velocity changes from \(u\) to \(v\) in time \(t\),

since \(a = \dfrac{v-u}{t}\). Writing the proportionality with a constant \(k\), \(F = kma\); the newton is defined so that \(k = 1\), giving \(F = ma\).

(c)(iii) Net (resultant) force \(= 9600 - 2200 = 7400\ \text{N}\). Acceleration