$(a)$ State Newton's third law of motion and give two examples to illustrate the law.
$(b)$ Calculate the force required to produce:
$(i)$ an acceleration of $2.5 \, m s^{-2}$ in a body of $4 \, kg$.
$(ii)$ an acceleration of $3 \, m s^{-2}$ in a body of $10 \, kg$.

(N/A) Newton's third law of motion states that, "To every action, there is always an equal and opposite reaction."
Examples:
$(i)$ Walking: When a person walks, they push the ground backward with their foot (action). The ground exerts an equal and opposite force on the foot (reaction), which pushes the person forward.
$(ii)$ Recoil of a boat: When a person jumps out of a boat, they push the boat backward (action). The boat exerts an equal and opposite force on the person, pushing them forward, while the boat moves backward (reaction).
$(b)$ Using the formula $F = m \times a$:
$(i)$ Given $m = 4 \, kg$ and $a = 2.5 \, m s^{-2}$.
$F = 4 \, kg \times 2.5 \, m s^{-2} = 10 \, N$.
$(ii)$ Given $m = 10 \, kg$ and $a = 3 \, m s^{-2}$.
$F = 10 \, kg \times 3 \, m s^{-2} = 30 \, N$.