← Theme A · Space, Time & Motion
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Theme A · Space, Time & Motion

Chapter 1 · Motion

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Velocity & acceleration
v=ΔsΔt,a=ΔvΔtv = \frac{\Delta s}{\Delta t},\quad a = \frac{\Delta v}{\Delta t}
Gradients on ss–tt and vv–tt graphs.
suvat (constant a)
v=u+at,    s=ut+12at2,    v2=u2+2as,    s=12(u+v)tv = u + at,\;\; s = ut + \tfrac{1}{2}at^2,\;\; v^2 = u^2 + 2as,\;\; s = \tfrac{1}{2}(u+v)t
Projectile motion
x:uxt  y:uyt−12gt2x: u_x t \quad\; y: u_y t - \tfrac{1}{2}gt^2
Horizontal & vertical independent; range max at 45°.
Newton's laws
∑F=ma\textstyle\sum F = ma
1st: inertia. 3rd: equal & opposite reaction.
Momentum & impulse
p=mv,FΔt=Δpp = mv,\quad F\Delta t = \Delta p
Total pp conserved in an isolated system.
Collisions
Elastic: KE conserved. Inelastic: KE lost; perfectly inelastic = stick together.
Work, KE, PE
W=Fscos⁡θ,    Ek=12mv2,    Ep=mghW = Fs\cos\theta,\;\; E_k = \tfrac{1}{2}mv^2,\;\; E_p = mgh
Work–energy theorem
Wnet=ΔEkW_{net} = \Delta E_k
Power & efficiency
P=Wt=Fv,η=EusefulEinP = \frac{W}{t} = Fv,\quad \eta = \frac{E_{useful}}{E_{in}}
η<1\eta < 1 always; efficiency has no unit (it's a ratio).
Scalar vs vector
Scalar: distance, speed, mass, energy. Vector: displacement, velocity, acceleration, force, momentum (need direction).
Resolving a vector
Fx=Fcos⁡θ,Fy=Fsin⁡θF_x = F\cos\theta,\quad F_y = F\sin\theta
Treat ⟂ directions independently. Resultant of ⟂ parts: Fx2+Fy2\sqrt{F_x^2+F_y^2}.
Projectile recipe
Horizontal: constant ux=ucos⁡θu_x=u\cos\theta. Vertical: suvat with a=−ga=-g. They share only the time tt. At the top vy=0v_y=0.
Free fall
v=2gh,h=12gt2v=\sqrt{2gh},\quad h=\tfrac12 g t^2
From rest; mass cancels (all objects fall the same, ignoring air resistance).
Newton's 3rd law
Forces come in equal & opposite pairs on DIFFERENT bodies — they never cancel on the same body.
Impulse–momentum
FΔt=Δp=mΔvF\Delta t = \Delta p = m\Delta v
Bigger Δt\Delta t (crumple zones) ⇒ smaller force for the same Δp\Delta p.
Elastic vs inelastic
Both conserve momentum. Elastic also conserves KE; inelastic loses KE (to heat/sound); perfectly inelastic = stick together.
Key SI units
vv: m s⁻¹ · aa: m s⁻² · FF: N (= kg m s⁻²) · pp: kg m s⁻¹ · E,WE,W: J · PP: W. ALWAYS convert to these before substituting.
Common traps
Forgetting g acts at the top of flight; using g instead of −g for sign; not converting g→kg or cm→m; dropping the unit in the final answer.
Constant
g≈9.81 m s−2  (use 10 if told)g \approx 9.81\ \text{m s}^{-2}\;(\text{use }10\text{ if told})