[tex]a) \\ \\ E_{k} = \frac{mv {}^{2} }{2} \: \: \: \: \: \: \: / \times 2 \\ \\ 2E_{k} = mv {}^{2} \: \: \: \: \: \: \: / \div v {}^{2} \\ \\ \frac{2E_{k}}{v {}^{2} } = m \\ \\ m = \frac{2E_{k}}{v {}^{2} } \\ \\ \\ 2E_{k} = mv {}^{2} \: \: \: \: \: \: \: / \div m \\ \\ \frac{2E_{k}}{m} = v {}^{2} \\ \\ v = \sqrt{ \frac{2E_{k}}{m} } \\ \\ \\ b) \\ \\ s = vt \: \: \: \: \: \: \: \: / \div t \\ \\ \frac{s}{t} = v \\ \\ v = \frac{s}{t} \\ \\ \\ s = vt \: \: \: \: \: \: / \div v \\ \\ \frac{s}{v} = t \\ \\ t = \frac{s}{v} \\ \\ \\ c) \\ \\ a = w {}^{2} r \: \: \: \: \: \: \: / \div w {}^{2} \\ \\ \frac{a}{w {}^{2} } = r \\ \\ r = \frac{a}{w {}^{2} } \\ \\ \\ a = w {}^{2} r \: \: \: \: \: \: \: \: / \div r \\ \\ \frac{a}{r} = w {}^{2} \\ \\ w = \sqrt{} \frac{a}{r} \\ \\ \\ d) \\ \\ F = ma \: \: \: \: \: / \div a \\ \\ \frac{F }{a} = m \\ \\ m = \frac{F }{a} \\ \\ \\ F = ma \: \: \: \: \: \: / \div m \\ \\ \frac{F}{m} = a \\ \\ a = \frac{F}{m} \\ \\ \\ e) \\ \\ s = \frac{at {}^{2} }{2} \: \: \: \: \: \: \: \: / \times 2 \\ \\ 2s = at {}^{2} \: \: \: \: \: \: / \div t {}^{2} \\ \\ \frac{2s}{t {}^{2} } = a \\ \\ a = \frac{2s}{t {}^{2} } \\ \\ \\ 2s = at {}^{2} \: \: \: \: \: \: \: \: / \div a \\ \\ \frac{2s}{a} = t {}^{2} \\ \\ t = \sqrt{ \frac{2s}{a} } \\ \\ \\ f) \\ \\ \frac{T _{1} }{v_{1}} = \frac{T_{1}}{ v_{2}} \: \: \: \: \: \: \: / \times v_{2} \\ \\ \frac{T_{1} v_{2}}{ v_{1}} = T_{2} \\ \\T_{2} = \frac{T_{1} v_{2}}{ v_{1}} \\ \\ \\T_{2} = \frac{T_{1} v_{2}}{ v_{1} } \: \: \: \: \: \: \: / \times v_{1} \\ \\T_{2} v_{1} = T _{1}v _{2} \: \: \: \: \: \: / \div T _{1} \\ \\ \frac{T _{2}v _{1}}{T _{1}} = v_{2} \\ \\ v _{2} = \frac{T _{2}v _{1}}{T _{1}} [/tex]
