1.) v = v 0 + a ⋅ t s = v 0 ⋅ t + 1 2 ⋅ a ⋅ t 2 {\displaystyle v=v_{0}+a\cdot t\qquad s=v_{0}\cdot t+{\frac {1}{2}}\cdot a\cdot t^{2}} v − v 0 = a ⋅ t {\displaystyle v-v_{0}=a\cdot t} t = v − v 0 a s = v 0 ⋅ ( v − v 0 ) a + a 2 ⋅ ( v − v 0 a ) 2 {\displaystyle t={\frac {v-v_{0}}{a}}\qquad s={\frac {v_{0}\cdot (v-v_{0})}{a}}+{\frac {a}{2}}\cdot \left({\frac {v-v_{0}}{a}}\right)^{2}} s = v 0 ⋅ ( v − v 0 ) a + a 2 ⋅ v 2 − 2 ⋅ v ⋅ v 0 + v 0 2 a 2 {\displaystyle s={\frac {v_{0}\cdot (v-v_{0})}{a}}+{\frac {a}{2}}\cdot {\frac {v^{2}-2\cdot v\cdot v_{0}+{v_{0}}^{2}}{a^{2}}}} s = v 0 ⋅ ( v − v 0 ) a + a ⋅ ( v 2 − 2 ⋅ v ⋅ v 0 + v 0 2 ) 2 a 2 {\displaystyle s={\frac {v_{0}\cdot (v-v_{0})}{a}}+{\frac {a\cdot (v^{2}-2\cdot v\cdot v_{0}+{v_{0}}^{2})}{2a^{2}}}} s = 2 v 0 ⋅ ( v − v 0 ) 2 a + v 2 − 2 ⋅ v ⋅ v 0 + v 0 2 2 a {\displaystyle s={\frac {2v_{0}\cdot (v-v_{0})}{2a}}+{\frac {v^{2}-2\cdot v\cdot v_{0}+{v_{0}}^{2}}{2a}}} s = 2 v 0 ⋅ v − 2 v 0 2 + v 2 − 2 ⋅ v ⋅ v 0 + v 0 2 2 a {\displaystyle s={\frac {2v_{0}\cdot v-{2v_{0}}^{2}+v^{2}-2\cdot v\cdot v_{0}+{v_{0}}^{2}}{2a}}} 2 a s = − 2 v 0 2 + v 0 2 + v 2 {\displaystyle 2as=-2{v_{0}}^{2}+{v_{0}}^{2}+v^{2}} v 2 − v 0 2 = 2 a s _ {\displaystyle {\underline {v^{2}-{v_{0}}^{2}=2as}}}
2.) a) s ( t ) = ( 72 t 2 + 12500000 ) 1 / 2 {\displaystyle s(t)=(72t^{2}+12500000)^{1/2}\,} s ′ ( t ) = 1 2 ⋅ ( 72 t 2 + 12500000 ) − 1 / 2 ⋅ 144 t {\displaystyle s'(t)={\frac {1}{2}}\cdot (72t^{2}+12500000)^{-1/2}\cdot 144t} v ( t ) = 72 t 72 t 2 + 12500000 {\displaystyle v(t)={\frac {72t}{\sqrt {72t^{2}+12500000}}}}
