1

v_avg = ΔxΔtv = lim_Δt→0 ΔxΔt = dxdta = dvdt = d²xdt²[v] = m/s,  [a] = m/s²

2

vf − vi = ∫tftia(t) dtxf − xi = ∫tftiv(t) dtv = v0 + atx = x0 + v0t + (1/2)at2Δx = 12a(v2 − v20)

3

v = gtd = (1/2)gt²d = v²2gv = 2gdg ≈ 9.8 m/s²

4

a(t) = sin tv(t) = −cos tx(t) = −sin ta(t) + x(t) = 0

5

x = r cos θ,  y = r sin θr = x² + y²,  tan θ = yx

6

Δr = (x_f − x_i, y_f − y_i)0 ≤ |Δr| = (x_f − x_i)² + (y_f − y_i)² ≤

7

A + B = (A_x + B_x, A_y + B_y)A + B = B + AA = A_xî + A_yĵcA = (cA_x, cA_y)

8

a = a²_x + a²_y = a²_x′ + a²_y′θ = θ′ + φ

9

A · B = AB cos θ = A_xB_x + A_yB_y + A_zB_z|A × B| = AB sin θA × B = (A_yB_z − A_zB_y, A_zB_x − A_xB_z, A_xB_y − A_yB_x)A × B = −B × A

10

F₁ + F₂ + F₃ = 0ΣF = ma = 0 ⇒ a = 0: 2 cos θ = 1 ⇒ θ = 60°

11

x = v_it cos θ_iy = v_it sin θ_i − (1/2)gt²y = x tan θ_i − gx²2v²_icos²θ_iR = v²_i sin 2θ_igh = v²_i sin²θ_i2g

12

13

a = −v²rr̂,  a = v²r = rω²v = rω,  ω = dθdtT = 2πrv = 2πω = 1fθ = sr

14

r_PA = r_PB + r_BAv_PA = v_PB + v_BAa_PA = a_PB