Linear motion (displacement, velocity, acceleration, suvat equations), Newton's three laws, free-body diagrams, momentum $p = mv$, impulse $J = F \Delta t$, work, energy, power

What this dot point is asking

QCAA wants Year 11 students to apply Newton's laws, momentum, energy and the SUVAT equations to linear motion problems.

SUVAT equations

For uniformly accelerated motion:

• IMATH_0
• IMATH_1
• IMATH_2
• IMATH_3

Where $u$ initial velocity, $v$ final, $a$ acceleration, $s$ displacement, $t$ time.

Newton's laws

1st law (inertia). Object at rest stays at rest; in motion stays in motion at constant velocity, unless acted on by net external force.

2nd law. $F = ma$. Net force equals mass times acceleration.

3rd law. Action-reaction pair: equal and opposite forces on different bodies.

Free-body diagrams

Show all forces on the object (gravity, normal force, friction, tension, applied). Sum vectorially, set equal to $ma$.

Momentum and impulse

$p = mv$ (kg m/s). Vector.

Impulse $J = F\Delta t = \Delta p$.

Conservation: in isolated system, total momentum conserved through collisions.

Energy

Work $W = Fd\cos\theta$.

Kinetic $KE = \frac{1}{2}mv^2$.

Gravitational PE $= mgh$.

Conservation of mechanical energy: $KE + PE =$ constant (no friction).

With friction: $KE_i + PE_i = KE_f + PE_f + E_{\text{lost}}$.

Power

$P = W/t = Fv$ (W = J/s).

Common errors

Substituting before differentiating (in derivative-like manipulations). Not relevant here but a related issue.

Confusing distance and displacement. Distance is path; displacement is net change.

Sign errors in free fall. Choose positive direction, stick to it.

Inelastic vs elastic. Momentum always conserved. Kinetic energy only in elastic.

In one sentence

Linear motion is analysed using suvat equations ($v = u + at$, $s = ut + \frac{1}{2}at^2$, $v^2 = u^2 + 2as$) and Newton's three laws (inertia, $F = ma$, action-reaction); momentum $p = mv$ is conserved in collisions (elastic also conserves $KE$, inelastic does not); work, kinetic energy ($\frac{1}{2}mv^2$), potential energy ($mgh$) and conservation of energy govern energy transfers.