Problem Solving of Rectilinear Equation ~ SanGeronimo Knowledge

T h e p a t h t a k e n b y a p a r t i c l e i s a h o r i z o n t a l l i n e a s i t

S t e p 1 : G e t t h e D e r i v a t i v e o f s = \frac{1}{6} t^{4} - \frac{7}{6} t^{3} - 7 t^{2} + \frac{1}{2} t + 1

v = \frac{2}{3} t^{3} - \frac{7}{2} t^{2} - 14 t + \frac{1}{2}

S t e p 2 : G e t t h e D e r i v a t i v e o f v = \frac{2}{3} t^{3} - \frac{7}{2} t^{2} - 14 t + \frac{1}{2}

a = 2 t^{2} - 7 t - 14

S t e p 3 : E q u a t e t h e a c c e l e r a t i o n t o o n e

2 t^{2} - 7 t - 14 = 1

S t e p 4 : W h e n t = 5 a t v = \frac{2}{3} t^{3} - \frac{7}{2} t^{2} - 14 t + \frac{1}{2}

a (5) = \frac{2}{3} (5)^{3} - \frac{7}{2} (5)^{2} - 14 (5) + \frac{1}{2}

F i n a l A n s w e r : t = 5, a (5) = - \frac{221}{3}

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