Question

give the solved explaination​

Answer 1

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Displacement \: of \: particle \: in \: n \: sec = s_{n} \\ \\ \tt: \implies Diplacement \: of \: particle \: in \: (n - 1) \: sec = s_{n - 1} \\ \\ \red{\underline \bold{To \: Show :}} \\ \tt: \implies s_{nth} = u + \frac{a}{2} (2n - 1)$

• According to given question :

$\tt \circ \: v_{(n - 1)} = Velocity \: at \: the \: begining \: of \: {(n - 1)}\: sec \\ \\ \tt \circ \: v_{n} = Velocity \: at \: the \: end \: of \: n \: sec \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v_{(n - 1)} = u + at \\ \\ \tt: \implies v_{(n - 1)} =u + a(n - 1) - - - - - (1) \\ \\ \bold{Similarly : } \\ \tt: \implies v_{n} =u + at \\ \\ \tt: \implies v_{n } =u + an - - - - - (2) \\ \\ \bold{For \: average \: velocity \: in \: {n}^{th} \: sec} \\ \tt: \implies v_{Avg} = \frac{v_{(n - 1)} + v_{n}}{2} \\ \\ \tt: \implies v_{Avg} = \frac{u + a(n - 1) + u + an}{2} \\ \\ \tt: \implies v_{Avg} = u + \frac{a}{2} (2n - 1) - - - - - (3) \\ \\ \bold{Distance \: traversed \: during \: this \: one \: sec} \\ \tt: \implies s_{nth} = v_{Avg} \times t \\ \\ \tt: \implies s_{nth} = \bigg(u + \frac{a}{2} (2n - 1) \bigg) \times 1 \\ \\ \green{\tt: \implies s_{nth} = u + \frac{a}{2} (2n - 1)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \green{ \huge{\boxed{\bold{Derived : }}}}$