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Kinematics, Newton's Laws & Work-Energy

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1. Kinematics and Newton's Second Law

Classical mechanics models translation and acceleration under net external forces, governing mechanical work and energy conservation.

Kinematic Equations

v = v₀ + at · s = v₀t + ½at² · v² = v₀² + 2as

Valid for linear motion with constant rectilinear acceleration

Newton's Second Law

F_net = m · a

Net unbalanced force accelerates mass proportionally in the direction of the vector

Work & Energy

W = F · d · cos(θ) · E_k = ½mv²

Work-energy theorem establishes that net work equals change in kinetic energy (W_net = ΔE_k)

Gravitational Potential

E_p = m · g · h

In conservative gravitational fields, total mechanical energy (E_k + E_p) remains constant

Worked example

1A 4.0 kg object accelerates from rest at a = 3.0 m/s² over a distance of d = 6.0 m.
2Find final velocity, net force, and work done.
3Net force F = m*a = 4.0 × 3.0 = 12 N.
4Final velocity v² = 0 + 2(3.0)(6.0) = 36 implies v = 6.0 m/s.
5Work W = F*d = 12 × 6.0 = 72 J (equal to final E_k = 0.5 × 4.0 × 6.0² = 72 J).

1.Newton's Second Law states that net force acting on a body equals m × a.

2.Kinetic energy of a body is directly proportional to its velocity.

3.Free-fall distance from rest under constant acceleration g is s = 0.5 g t².

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