קינמטיקה

✦ בנוי על ידי פהד גאנם ✦

Δx = x₂ − x₀   |   d = |Δx|   |   s = |Δx₁| + |Δx₂|   |   sd ≥ 1
+2.0 m
+8.0 m
−1.0 m
0.00
0.00
0.00
—
+2.0
+8.0
−1.0
+2.0

Δx = x₂ − x₀ = (−1) − (2) = −3 m
d = |Δx| = |−3| = 3 m
s = |8 − 2| + |(−1) − 8| = 6 + 9 = 15 m
sd = 153 = 5


x(t) = x₀ + v·t   |   x(t) = x₀ + v₀·t + 12a·t²
4.0 m
2.0 m/s
0.00
0.00
0.00
0.00

x(t) = x₀ + v·t  ,  x₀ = 4 m
v = x₂ − x₁t₂ − t₁ = (−6) − 45 − 0 = −105 = −2 m/s
x(t) = 4 − 2·t
0 = 4 − 2·t  →  t = 42 = 2 s

v = ΔxΔt   |   Δx = v·Δt   |   vavg = Σ ΔxΣ Δt
3.0 m/s
4.0 s
1.0 m/s
2.0 s
4.0 m/s
3.0 s
0.00
0.00
0.00
0.00
0.00
0.00
0.00

Δx₁ = 60 · 2 = 120 km Δx₂ = 90 · 1 = 90 km
Σ Δx = 120 + 90 = 210 km Σ Δt = 2 + 1 = 3 h
vavg = Σ ΔxΣ Δt = 210 km3 h = 70 km/h
60 + 902 = 75 km/h ≠ 70 km/h

v̄ = ΔxΔt = x(t₂) − x(t₁)t₂ − t₁   |   v(t) = limΔt→0 ΔxΔt
1.00 s
4.00 s
2.0 m/s²
1.0 m/s
0.00
0.00
0.00
0.00
0.00
0.00
0.00

x(1) = 2·1² + 3·1 = 5 m x(3) = 2·3² + 3·3 = 27 m
v̄ = x(3) − x(1)3 − 1 = 27 − 52 = 222 = 11 m/s
v(t) = 4t + 3  →  v(2) = 4·2 + 3 = 11 m/s
tm = t₁ + t₂2 = 1 + 32 = 2 s

v = v₀ − g·t   |   y = y₀ + v₀·t − 12g·t²   |   v² = v₀² − 2g·(y − y₀)
45 m
20 m/s
2.0 kg
0.00
0.0
0.00
0.00
0.00
45.0
0.00
0.00

y = y₀ − 12g·t² y₀ = 12g·t²
t = √2y₀g = √2 · 459.8 = √9.18 = 3.03 s
v = g·t = 9.8 · 3.03 = 29.70 m/s
0 = v₀² − 2g·h  →  h = v₀²2g = 40019.6 = 20.41 m

ā = ΔvΔt = v₂ − v₁t₂ − t₁   |   a(t) = dvdt   |   v(t) = v₀ + k·t³  →  a(t) = 3k·t²
0.0 s
4.0 s
4.00 s
0.50 m/s⁴
4.00
36.00
32.00
4.00
8.00
24.00
16.00
36.00

v(t) = 4 + 0.5·t³ v(0) = 4 + 0.5·0³ = 4.00 m/s v(4) = 4 + 0.5·64 = 4 + 32 = 36.00 m/s
ā = v₂ − v₁t₂ − t₁ = 36.00 − 4.004 − 0 = 32.004 = 8.00 m/s²
a(t) = dvdt = 3 · 0.5 · t² = 1.5·t² a(4) = 1.5 · 4² = 1.5 · 16 = 24.00 m/s²
Δa = a(4) − ā = 24.00 − 8.00 = 16.00 m/s²

Rx = Ax + Bx   |   Ry = Ay + By
R = √(Rx² + Ry²)   |   θ = tan⁻¹RyRx
3.0
0°
4.0
90°
1.0
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.0
0.00
0.00
0.00
0.00

Rx = 3.0 + 0 = 3.0 km   |   Ry = 0 + 4.0 = 4.0 km
R = √(Rx² + Ry²) = √(3.0² + 4.0²) = √25 = 5.0 km
θ = tan⁻¹RyRx = tan⁻¹4.03.0 = tan⁻¹(1.333) = 53.1°
s = 3.0 + 4.0 = 7.0 km

a_r = v²r   |   a = √(a_t² + a_r²)   |   θ = tan⁻¹a_ta_r
50 m
15.0 m/s
2.0 m/s²
0.00
0.00
0.00
0.0
0.00

r = 50 m  |  v = 15 m/s  |  a_t = 2.0 m/s²
a_r = v²r = (15)²50 = 4.5 m/s²
a = √(a_t² + a_r²) = √(2.0² + 4.5²) = √24.25 = 4.92 m/s²
θ = tan⁻¹a_ta_r = tan⁻¹2.04.5 = tan⁻¹(0.444) = 24.0°
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