W - praca Ek - energia mech. na końcu Ep - energie mech. na początku W= Ek-Ep Ek = W + Ep [latex]frac{[latex]mVk^{2}[/latex]}{2}[/latex] = W + [latex]frac{[latex]mVp^{2}[/latex]}{2}[/latex] | *2 [latex]mVk^{2}[/latex] = 2W + [latex]mVp^{2}[/latex] [latex]Vk^{2}[/latex] = [latex]frac{2W + [latex]mVp^{2}[/latex]}{m}[/latex] Vk = [latex]sqrt{ [latex]frac{2W + [latex]mVp^{2}[/latex]}{m}[/latex]}[/latex] Vk = [latex]sqrt{ [latex]frac{2*206250 J + [latex]1500 kg * (25 m/s)^{2}[/latex]}{1500 kg}[/latex]}[/latex] Vk = [latex]sqrt{ [latex]frac{412500 J + 937500 J }{1500 kg}[/latex]}[/latex] Vk = [latex]sqrt{ [latex]frac{135000 J }{1500 kg}[/latex]}[/latex] Vk = [latex]sqrt{ 900[latex]frac{[latex]m^{2}[/latex]}{[latex]s^{2}[/latex]}[/latex] }[/latex] Vk= 30 m/s = 108 km/h
m=1500kg v₁=25m/s W=206250J Ek=0,5mv² Ek₁=0,5·1500kg·(25m/s)²=468750J Ek₂=468750J+206250J=675000J 675000J=0,5·1500kg·v₂² v₂²=900m²/s² v₂=30m/s Odp.: Prędkość samochodu wynosi 30m/s.
