Question

Please solve it ASAP​

Answer 1

Explanation:

$x _{1} \: \: \: \: t_{1} \: \: \: \: v_{1} \\ \\ \\ x _{2} \: \: \: \: t_{2} \: \: \: \: v_{2} \\ \\ \\ x _{3} \: \: \: \: t_{3} \: \: \: \: v_{3} \\ \\ \\ v_{2} = v_{1} + a(t_{2} - t_{1}) \\ \\ \\ v_{3} = v_{1} + a(t_{3} - t_{1}) \\ \\ \\ ((x _{2} - x _{1}) = v _{1}(t _{2} - t _{1}) + \dfrac{1}{2} a(t _{2} - t _{1})^{2} ) \times (t _{3} - t _{1}) \\ \\ \\ ((x _{3} - x _{1}) = v _{1}(t _{3} - t _{1}) + \dfrac{1}{2} a(t _{3} - t _{1})^{2} ) \times (t _{2} - t _{1}) \\ \\ \\ substituting \\ \\ \\ (x _{2} - x _{1}) (t _{3} - t _{1}) = \dfrac{1}{2} a(t _{3} - t _{1})(t _{2} - t _{1})(t _{2} - t _{1} - t _{3} + t _{1}) - (x _{3} - x_{1})(t _{2} - t _{2}) \\ \\ \\ a = 2 \dfrac{((x_{2} - x _{1})(t _{3} - t _{1}) - (x_{3} - x _{1})(t_{2} - t _{1}))}{(t _{2} - t_{3}) (t _{3} - t_{1})( t _{2} -t _{1})} \\ \\ \\ a = 2 (\dfrac{(x_{2} - x _{3}) t _{1} + (x_{3} - x _{1})t_{2} + (x_{1} - x _{3} )t_{3} }{(t _{2} - t_{3}) (t _{3} - t_{1})( t _{1} -t _{2})} )$