Newton’s second law — correct equation form: If P is the net force on a body of mass m producing acceleration a, which one of the following equations correctly states Newton’s second law?

Introduction / Context:
Newton’s second law connects dynamics (forces) with kinematics (acceleration). It is foundational for solving virtually all engineering mechanics problems from particle motion to rigid-body dynamics.

Given Data / Assumptions:

• P is the resultant (net) force acting on the body.
• m is the mass of the body (assumed constant).
• a is the linear acceleration in the direction of P.

Concept / Approach:
The standard vector form is P = m * a. Rearranged to one side for equation checking, P − m * a = 0 is the correct identity. Any other algebraic or dimensional manipulation in the options that violates this equality is incorrect.

Step-by-Step Solution:
Recall Newton’s second law: P = m * a.Move all terms to one side: P − m * a = 0.Compare with given choices; pick the expression that matches.Therefore, the correct option is P − m.a = 0.

Verification / Alternative check:
Dimensional consistency: [P] = N = kgm/s^2 and [ma] = kg*(m/s^2) = N; subtracting like dimensions is valid, confirming the identity structure P − ma = 0.

Why Other Options Are Wrong:

• P + m.a = 0: implies P = −ma; sign is wrong for the general statement.
• P x m.a = 0: “x” suggests multiplication or a cross-product; not the law’s form and dimensions become N^2.
• P/m.a = 0: division gives a dimensionless number; cannot equal zero identically for all cases.

Common Pitfalls:

• Forgetting that P is the net force (not a single applied force), i.e., include all forces to compute m*a.

Final Answer:
P - m.a = 0