Samenvatting Formularium algemene fysica

1


Hoofdstuk 2: 1-dim kinematica
Verplaatsing:
∆𝑥 = 𝑥𝑓 − 𝑥𝑖 ∆𝑥 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔 [m]
𝑥𝑓 = 𝑓𝑖𝑛𝑎𝑙𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]
𝑥𝑖 = 𝑖𝑛𝑖𝑡𝑖ë𝑙𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]


Gemiddelde snelheid:
∆𝑥 𝑥𝑓 − 𝑥𝑖 𝑣𝑎𝑣 = 𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑣𝑎𝑣 = =
∆𝑡 𝑡𝑓 − 𝑡𝑖 ∆𝑥 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑠𝑖𝑛𝑔 [m]
∆𝑡 = 𝑡𝑖𝑗𝑑𝑠𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 [s]
Ogenblikkelijke snelheid:
∆𝑥 𝑑𝑥 𝑣 = 𝑜𝑔𝑒𝑛𝑏𝑙𝑖𝑘𝑘𝑒𝑙𝑖𝑗𝑘𝑒 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑣 = lim =
∆𝑡→0 ∆𝑡 𝑑𝑡 𝑑𝑥
= 𝑎𝑓𝑔𝑒𝑙𝑒𝑖𝑑𝑒 𝑣𝑎𝑛 𝑥(𝑡) − 𝑔𝑟𝑎𝑓𝑖𝑒𝑘
𝑑𝑡

Gemiddelde versnelling
Δ𝑣 𝑣𝑓 − 𝑣𝑖 𝑎𝑎𝑣 = 𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 [m/s²]
𝑎𝑎𝑣 = =
Δ𝑡 𝑡𝑓 − 𝑡𝑖 ∆𝑣 = 𝑣𝑒𝑟𝑎𝑛𝑑𝑒𝑟𝑖𝑛𝑔 𝑖𝑛 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
∆𝑡 = 𝑣𝑒𝑟𝑎𝑛𝑑𝑒𝑟𝑖𝑛𝑔 𝑖𝑛 𝑡𝑖𝑗𝑑 [s]
Ogenblikkelijke versnelling
∆𝑣 𝑑𝑣 𝑎 = 𝑜𝑔𝑒𝑛𝑏𝑙𝑖𝑘𝑘𝑒𝑙𝑖𝑗𝑘𝑒 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 [m/s²]
𝑎 = lim =
∆𝑡→0 ∆𝑡 𝑑𝑡 𝑑𝑣
= 𝑎𝑓𝑔𝑒𝑙𝑒𝑖𝑑𝑒 𝑣𝑎𝑛 𝑑𝑒 𝑣(𝑡) − 𝑔𝑟𝑎𝑓𝑖𝑒𝑘
𝑑𝑡

EVRB: snelheid
𝑣 = 𝑣0 + 𝑎 𝑡 𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑣0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑎 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 [m/s²]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
EVRB: verplaatsing
1 2 𝑥 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔 𝑜𝑓 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]
𝑥 = 𝑥0 + 𝑣0 𝑡 + 𝑎𝑡
2 𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]
𝑣0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 [m/s²]
EVRB: v in functie van x
𝑣 2 = 𝑣02 + 2𝑎(𝑥 − 𝑥0 ) 𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑣0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑎 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 [m/s²]
𝑥 = 𝑓𝑖𝑛𝑎𝑙𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]
𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]
𝑥 − 𝑥0 = ∆𝑥 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔 [m]
Vrije val vanuit rust: positie
1 𝑥 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]
𝑥 = 𝑔𝑡²
2 𝑔 = 𝑣𝑎𝑙𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 = 9 · 81 𝑚/𝑠²
𝑡 = 𝑡𝑖𝑗𝑑 [s]

, 2




Vrije val vanuit rust: snelheid
𝑣 = 𝑔𝑡 𝑜𝑓 𝑣 = √2𝑔𝑥 𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑔 = 𝑣𝑎𝑙𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 = 9 · 81 𝑚/𝑠²
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑥 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 [m]




Vrije val na opwaartse worp: landingstijd
2𝑣0 𝑡 = 𝑙𝑎𝑛𝑑𝑖𝑛𝑔𝑠𝑡𝑖𝑗𝑑 [s]
𝑡𝑙𝑎𝑛𝑑𝑖𝑛𝑔𝑠𝑡𝑖𝑗𝑑 =
𝑔 𝑣0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑔 = 𝑣𝑎𝑙𝑣𝑒𝑟𝑛𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 = 9 · 81 𝑚/𝑠²



Hoofdstuk 3: Vectoren
Scalair product/dot product van 2 vectoren
⃗⃗⃗ = |𝑣⃗|⌈𝑤
𝑣⃗ · 𝑤 ⃗⃗⃗⌉ cos 𝜃 = 𝑣𝑤 cos 𝜃 𝑣⃗ = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑣𝑎𝑛 𝑣
𝑤
⃗⃗⃗ = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑣𝑎𝑛 𝑤
|𝑣⃗| = 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑤𝑎𝑎𝑟𝑑𝑒 𝑣𝑎𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝑣 (𝑣𝑒𝑐𝑡𝑜𝑟 𝑘𝑎𝑛 + 𝑜𝑓 − 𝑧𝑖𝑗𝑛)
|𝑤
⃗⃗⃗| = 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑤𝑎𝑎𝑟𝑑𝑒 𝑣𝑎𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝑤 (𝑣𝑒𝑐𝑡𝑜𝑟 𝑘𝑎𝑛 + 𝑜𝑓 − 𝑧𝑖𝑗𝑛)
𝜃 = ℎ𝑜𝑒𝑘 𝑚𝑒𝑡 𝑑𝑒 𝑥 − 𝑎𝑠 [°]
Loodrechte vectoren
𝑣⃗ · 𝑤
⃗⃗⃗ = 0 𝑣⃗ = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑣𝑎𝑛 𝑣
𝑤
⃗⃗⃗ = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑣𝑎𝑛 𝑤
Vectorieel product van 2 vectoren
|𝐶⃗| = 𝐴𝐵 sin 𝜃 |𝐶⃗| = 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑤𝑎𝑎𝑟𝑑𝑒 𝑣𝑎𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝐶 (𝐶 𝑘𝑎𝑛 + 𝑜𝑓 − 𝑧𝑖𝑗𝑛)
𝜃 = ℎ𝑜𝑒𝑘 𝑡𝑢𝑠𝑠𝑒𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝐴 𝑒𝑛 𝑣𝑒𝑐𝑡𝑜𝑟 𝐵 [°]
Gemiddelde snelheid
⃗⃗⃗⃗⃗
∆𝑟 𝑣⃗𝑎𝑣 = 𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑𝑠𝑣𝑒𝑐𝑡𝑜𝑟 [m/s]
𝑣⃗𝑎𝑣 =
∆𝑡 ⃗⃗⃗⃗⃗
∆𝑟 = ⃗⃗⃗⃗⃗
∆𝑥 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔𝑠𝑣𝑒𝑐𝑡𝑜𝑟 [m]
∆𝑡 = 𝑡𝑖𝑗𝑑𝑠𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 [s]
Ogenblikkelijke snelheid
⃗⃗⃗⃗⃗
∆𝑟 𝑑𝑟⃗ 𝑣⃗ = 𝑜𝑔𝑒𝑛𝑏𝑙𝑖𝑘𝑘𝑒𝑙𝑖𝑗𝑘𝑒 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑𝑠𝑣𝑒𝑐𝑡𝑜𝑟 [m/s]
𝑣⃗ = lim =
∆𝑡→0 ∆𝑡 𝑑𝑡 ⃗⃗⃗⃗⃗
∆𝑟 = ⃗⃗⃗⃗⃗
∆𝑥 = 𝑣𝑒𝑟𝑠𝑐ℎ𝑖𝑙 𝑖𝑛 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔𝑠𝑣𝑒𝑐𝑡𝑜𝑟𝑒𝑛 [m]
𝑑𝑟⃗
= 𝑎𝑓𝑔𝑒𝑙𝑒𝑖𝑑𝑒 𝑣𝑎𝑛 𝑑𝑒 𝑣𝑒𝑐𝑡𝑜𝑟𝑖ë𝑙𝑒 𝑟(𝑡) − 𝑔𝑟𝑎𝑓𝑖𝑒𝑘
𝑑𝑡

Gemiddelde versnellingsvector
⃗⃗⃗⃗⃗
∆𝑣 𝑎⃗𝑎𝑣 = 𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔𝑠𝑣𝑒𝑐𝑡𝑜𝑟 [m/s²]
𝑎⃗𝑎𝑣 =
∆𝑡 ⃗⃗⃗⃗⃗ = 𝑣𝑒𝑟𝑠𝑐ℎ𝑖𝑙 𝑖𝑛 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑𝑠𝑣𝑒𝑐𝑡𝑜𝑟𝑒𝑛 [m/s]
∆𝑣
∆𝑡 = 𝑡𝑖𝑗𝑑𝑠𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 [s]
Ogenblikkelijke versnellingsvector
∆𝑣 𝑑𝑣⃗ 𝑎⃗ = 𝑜𝑔𝑒𝑛𝑏𝑙𝑖𝑘𝑘𝑒𝑙𝑖𝑗𝑘𝑒 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔𝑠𝑣𝑒𝑐𝑡𝑜𝑟 [m/s²]
𝑎⃗ = lim =
∆𝑡→0 ∆𝑡 𝑑𝑡 𝑑𝑣⃗⃗
= 𝑎𝑓𝑔𝑒𝑙𝑒𝑖𝑑𝑒 𝑣𝑎𝑛 𝑑𝑒 𝑣𝑒𝑐𝑡𝑜𝑟𝑖ë𝑙𝑒 𝑣(𝑡) − 𝑔𝑟𝑎𝑓𝑖𝑒𝑘
𝑑𝑡

, 3




Hoofdstuk 4: 2-dim kinematica
Positie in functie van de tijd
1 𝑥 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑥 − 𝑎𝑠 [m]
𝑥 = 𝑥0 + 𝑣0𝑥 𝑡 + 𝑎𝑥 𝑡²
2 𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑥 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s²]
1 𝑦 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
𝑦 = 𝑦0 + 𝑣0𝑦 𝑡 + 𝑎𝑦 𝑡²
2 𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
𝑣𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑦 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s²]


Snelheid in functie van de tijd
𝑣𝑥 = 𝑣0𝑥 + 𝑎𝑥 𝑡 𝑣𝑥 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑥 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s²]
𝑣𝑦 = 𝑣0𝑦 + 𝑎𝑦 𝑡 𝑣𝑦 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑣𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑦 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s²]
Snelheid in functie van de positie
𝑣𝑥2 = 𝑣0𝑥
2
+ 2𝑎𝑥 ∆𝑥 𝑣𝑥 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑎𝑥 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s²]
∆𝑥 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m]
𝑣𝑦2 = 𝑣0𝑦
2
+ 2𝑎𝑦 ∆𝑦 𝑣𝑦 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑣𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑎𝑦 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s²]
∆𝑦 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
Kogelbaan: positie in functie van de tijd (ax = 0; ay = -g)
𝑥 = 𝑥0 + 𝑣0𝑥 𝑡 𝑥 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m]
𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
(𝑎𝑥 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 = 0) [m/s²]
𝑡 = 𝑡𝑖𝑗𝑑 [s]

, 4


1 𝑦 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
𝑦 = 𝑦0 + 𝑣0𝑦 𝑡 − 𝑔𝑡²
2 𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
𝑣𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑦 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 = −𝑔 = −9 · 81 𝑚/𝑠²


Kogelbaan: snelheid in functie van de tijd (ax = 0; ay = -g)
𝑣𝑥 = 𝑣0𝑥 𝑣𝑥 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑦 = 𝑣0𝑦 − 𝑔𝑡 𝑣𝑦 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑣𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]


Kogelbaan: snelheid in functie van de positie ax = 0; ay = -g)
𝑣𝑥2 = 𝑣0𝑥
2
𝑣𝑥 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑦2 = 𝑣0𝑦
2
− 2𝑔∆𝑦 𝑣𝑦 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑣𝑦0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑎𝑦 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 = −𝑔 = −9 · 81 𝑚/𝑠 2
∆𝑦 = 𝑣𝑒𝑟𝑝𝑙𝑎𝑎𝑡𝑠𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
Horizontale lancering: positie in functie van de tijd (x0 = 0; y0 = h; vx0 = v0; vy0 = 0)
𝑥 = 𝑣0𝑥 𝑡 𝑥 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑥 − 𝑎𝑠 [m]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]

1
𝑦 = ℎ − 𝑔𝑡² (v0y = v0 sin 0° = 0) 𝑦 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
2
𝑦0 = ℎ = 𝑏𝑒𝑔𝑖𝑛𝑝𝑜𝑠𝑖𝑡𝑖𝑒 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑦 = −𝑔 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 = −9 · 81 𝑚/𝑠 2
Horizontale lancering : snelheid in functie van de tijd (x0 = 0; y0 = h; vx0 = v0; vy0 = 0)
𝑣𝑥 = 𝑣0 − 𝑔𝑡 𝑣0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑥 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]
𝑎𝑥 = −𝑔 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 = −9.81 𝑚/𝑠 2
𝑣𝑦 = −𝑔𝑡 𝑣𝑦 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 [m/s]
𝑎𝑦 = 𝑣𝑒𝑟𝑠𝑛𝑒𝑙𝑙𝑖𝑛𝑔 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑦 − 𝑎𝑠 = −𝑔 = −9.81 𝑚/𝑠 2
𝑡 = 𝑡𝑖𝑗𝑑 [s]
Horizontale lancering: snelheid in functie van de positie (x 0 = 0; y0 = h; vx0 = v0; vy0 = 0)
𝑣𝑥2 = 𝑣0𝑥
2
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑣𝑥 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑣𝑥0 = 𝑏𝑒𝑔𝑖𝑛𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣𝑜𝑙𝑔𝑒𝑛𝑠 𝑑𝑒 𝑥 − 𝑎𝑠 [m/s]
𝑡 = 𝑡𝑖𝑗𝑑 [s]