if an object moves along a straight line according to the relationship( x(t)=((1/2)t^2 −t+2)) find (1) the average speed between (x=(3/2) , x=(7/2)) (2) the pelvic velocity between (x=(7/2))


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Question Number 103703 by mohammad17 last updated on 16/Jul/20

$i f a n o b j e c t m o v e s a l o n g a s t r a i g h t l i n e$ $a c c o r d i n g t o t h e r e l a t i o n s h i p (x (t) = (\frac{1}{2} t^{2} - t + 2))$ $f i n d$ $(1) t h e a v e r a g e s p e e d b e t w e e n (x = \frac{3}{2}, x = \frac{7}{2})$ $(2) t h e p e l v i c v e l o c i t y b e t w e e n (x = \frac{7}{2})$
	Answered by Dwaipayan Shikari last updated on 16/Jul/20

	$A v e r a g e v e l o c i t y = \frac{△ S}{△ t} = \frac{2}{2} = 1 \frac{m}{s}$ $△ S = 2$ $\frac{3}{2} = \frac{1}{2} t_{1}^{2} - t_{1} + 2 (a t x = \frac{3}{2})$ $t_{1} = 1$ $\frac{7}{2} = \frac{1}{2} t_{2}^{2} - t_{2} + 2$ $t_{2} = 3 s o △ t = 2$ $I n s t a n t a n e o u s s p e e d x = \frac{7}{2} i s a t t = 3$ $\frac{d (x (t))}{d t} = t - 1 = 3 - 1 = 2 \frac{m}{s}$
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