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Question Number 61112 by Kunal12588 last updated on 29/May/19

Commented by Kunal12588 last updated on 29/May/19

$d r a w t h e g r a p h p l s$
Commented by Kunal12588 last updated on 29/May/19

Commented by Kunal12588 last updated on 29/May/19

$i s t h i s w r o n g i f y e s t h e n p l s d r a w t h e g r a p h .$
Commented by mr W last updated on 29/May/19

$i t h i n k y o u r g r a p h i s n o t c o r r e c t .$ ${i t}^{'} s m o r e c h a l l e n g i n g t o d r a w t h e$ $s - t, v - t a n d a - t g r a p h s .$
	Answered by tanmay last updated on 29/May/19

	$a = \frac{d v}{d t} = \frac{d v}{d s} \times \frac{d s}{d t} = v \times \frac{d v}{d s}$ $u p t o s = 100 m e t e r \to \frac{d v}{d s} = m = t a n θ = \frac{40 - 0}{100 - 0} = \frac{2}{5}$ $e q n o f v - s g r a p h u p t o s = 100$ $v = \frac{2}{5} \times s \to [y = m x]$ $s o w h e n s = 50 v = \frac{2}{5} \times 50 = 20$ $a = v \times \frac{d v}{d s} = 20 \times \frac{2}{5} = 8 m / {s e c}^{2}$ $e q n v - s g r a p h w h e n s \in [100, 200]$ $u s i n g (y - y_{1}) = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$ $(100, 40) a n d (200, 50) [x \to s y \to v]$ $v - 40 = \frac{50 - 40}{200 - 100} (s - 100)$ $v = 40 + \frac{1}{10} (s - 100) \to s o s l o p e = \frac{d v}{d s} = \frac{1}{10}$ $v = 40 + \frac{1}{10} (150 - 100)$ $v = 45$ $a = v \times \frac{d v}{d s}$ $= 45 \times \frac{1}{10} = 4.5 m / {s e c}^{2}$ $p l s c h e c k . . .$ $n o w w h e n s = 50 a = 8$ $e h e n s = 150 a = 4.5$ $s o a - s w i l l b e a s t r a i g h t l i n e$ $s \to a l o n g x a x i s a \to a l o n g y a x i s$ $e q n \to u s i n g (y - y_{1}) = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$ $(a - 8) = \frac{4.5 - 8}{150 - 50} (s - 50)$ $a - 8 = \frac{3.5}{100} (s - 50)$ $a = 0.035 s + 8 - \frac{3.5}{2}$ $a = 0.035 s + 6.25$
	Commented by Kunal12588 last updated on 29/May/19

	Commented by Kunal12588 last updated on 29/May/19

	$s o t h e g r a p h s h o u l d b e l i k e t h i s ?$
	Commented by tanmay last updated on 29/May/19

	Commented by tanmay last updated on 29/May/19

	$y e s i a m i n t e l e g r a m$
	Commented by Kunal12588 last updated on 29/May/19
	https://t.me/kunal1234523
	Answered by mr W last updated on 30/May/19

	$v = \frac{d s}{d t}$ $a = \frac{d v}{d t} = \frac{d s}{d t} \times \frac{d v}{d s} = v \frac{d v}{d s}$ $p h a s e 1 : f r o m s = 0 t o 100 :$ $\frac{d v}{d s} = \frac{40}{100} = \frac{2}{5}$ $v = \frac{2}{5} s$ $a = \frac{2}{5} \times \frac{2}{5} s = \frac{4}{25} s$ $a t s = 0 : a = 0 \times \frac{2}{5} = 0$ $a t s = 50 : a = 20 \times \frac{2}{5} = 8$ $a t s = 100 : a = 40 \times \frac{2}{5} = 16$ $p h a s e 2 : f r o m s = 100 t o 200 :$ $\frac{d v}{d s} = \frac{50 - 40}{200 - 100} = \frac{1}{10}$ $v = 40 + \frac{(s - 100) \times 10}{100} = 30 + \frac{s}{10}$ $a = \frac{1}{10} (30 + \frac{s}{10}) = 3 + \frac{s}{100}$ $a t s = 100 : a = 40 \times \frac{1}{10} = 4$ $a t s = 150 : a = 45 \times \frac{1}{10} = 4.5$ $a t s = 200 : a = 50 \times \frac{1}{10} = 5$
	Commented by mr W last updated on 29/May/19

	Commented by mr W last updated on 29/May/19

	$i n p h a s e 1 t h e f o r c e a p p l i e d o n t h e$ $o b j e c t i s i n c r e a s e d g r a d u a l l y . a t$ $s = 100, a n i m p a c t i s a p l l i e d o n t h e$ $o b j e c t i n i n v e r s e d d i r e c t i o n . a f t e r$ $t h a t i n p h a s e 2 t h e f o r c e a p p l i e d o n$ $t h e o b j e c t i s i n c r e a s e d a g a i n g r a d u a l l y .$
	Commented by Kunal12588 last updated on 30/May/19

	$t h a n k y o u s i r$ $s o m y f i r s t p h a s e f o r s \in [0, 100] w a s c o r r e c t .$
	Commented by Kunal12588 last updated on 30/May/19

	$s i r, v = 30 + \frac{s}{10}$ $a = \frac{1}{10} (30 + \frac{s}{10}) = 3 + \frac{s}{100}$
	Commented by mr W last updated on 30/May/19

	$y e s .$ $t h a n k s .$
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