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Question Number 57084 by frimpshaddie last updated on 30/Mar/19

Commented by Kunal12588 last updated on 30/Mar/19

$(d) w h e n t h e v e l o c i t y o f p a r t i c l e b e c o m e s 0$ $t h e n t h e p a r t i c l e i s s a i d t o b e i n r e s t$ $(h o r i z o n t a l m o t i o n o n l y)$ $∴ v = 0$ $\Rightarrow 3 t^{2} - 6 t = 0$ $\Rightarrow 3 t (t - 2) = 0$ $\Rightarrow t = 0 o r t = 2$ $a t t = 0 s$ $s = {(0)}^{3} - 2 {(0)}^{2} + 1 = 1 m$ $a t t = 2 s$ $s = {(2)}^{3} - 2 {(2)}^{2} + 1 = 8 - 8 + 1 = 1 m$ $w h e n : - t i m e i s e q u a l t o 0 s o r 2 s$ $w h e r e : - d i s t a n c e i s e q u a l t o 1 m$
Commented by kkc last updated on 30/Mar/19


	Answered by Kunal12588 last updated on 30/Mar/19

	$(a) v = \frac{d s}{d t} = \frac{d}{d t} (t^{3} - 2 t^{2} + 1)$ $\Rightarrow v = 3 t^{2} - 6 t$ $t = 2 s$ $\Rightarrow v = 3 {(2)}^{2} - 6 (2) = 0 {m s}^{- 1}$
	Answered by Kunal12588 last updated on 30/Mar/19

	$(b) v_{a v} = \frac{s_{f i n a l} - s_{i n i t i a l}}{t_{f i n a l} - t_{i n i t i a l}}$ $t_{i n i t i a l} = 0 s$ $s_{i n i t i a l} = {(0)}^{3} - 2 {(0)}^{2} + 1 = 1 m$ $t_{f i n a l} = 3 s$ $s_{f i n a l} = {(3)}^{3} - 2 {(3)}^{2} + 1 = 27 - 18 + 1 = 10 m$ $∴ v_{a v} = \frac{10 - 1}{3 - 0} = \frac{9}{3} = 3 {m s}^{- 1}$
	Answered by Kunal12588 last updated on 30/Mar/19

	$(c) a_{a v} = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}$ $v = 3 t^{2} - 6 t$ $t_{2} = 3 s$ $\Rightarrow v_{2} = 3 {(3)}^{2} - 6 (3) = 27 - 18 = 9 {m s}^{- 1}$ $t_{1} = 1 s$ $v_{1} = 3 {(1)}^{2} - 6 (1) = 3 - 6 = - 3 {m s}^{- 1}$ $∴ a_{a v} = \frac{9 - (- 3)}{3 - 1} = \frac{12}{2} = 6 {m s}^{- 2}$
	Answered by kkc last updated on 30/Mar/19


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