An object constrained to move along the x-axis is acted upon by a force F(x) where a=5N/m, b=−2N/m. F(x)=ax+bx^2 The object is observed to proceed directly from x=1m to x=3m. How much work was done by the object by the force?Does the process of integration take into account the fact that the force F(x) changes sign in interval.


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Question Number 25307 by NECx last updated on 08/Dec/17

$A n o b j e c t c o n s t r a i n e d t o m o v e$ $a l o n g t h e x - a x i s i s a c t e d u p o n b y$ $a f o r c e F (x) w h e r e a = 5 N / m,$ $b = - 2 N / m . F (x) = a x + {b x}^{2}$ $T h e o b j e c t i s o b s e r v e d t o p r o c e e d$ $d i r e c t l y f r o m x = 1 m t o x = 3 m .$ $H o w m u c h w o r k w a s d o n e b y t h e$ $o b j e c t b y t h e f o r c e ? D o e s t h e$ $p r o c e s s o f i n t e g r a t i o n t a k e i n t o$ $a c c o u n t t h e f a c t t h a t t h e f o r c e$ $F (x) c h a n g e s s i g n i n i n t e r v a l .$
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