How do i make the graphs of position vs velocity or acceleration vs velocity or position vs acceleration graphs. How to judge the turning point of the graph and check if it is decreasing or increasing.

Asked by laxmikant mishra | 15th Jul, 2014, 06:27: PM

Expert Answer:

G e n e r a l l y comma space p o s i t i o n space v e c t o r space i s space d e n o t e d space b y space apostrophe x apostrophe comma space v e l o c i t y space b y space fraction numerator d y over denominator d x end fraction comma space a c c e l e r a t i o n space b y space fraction numerator d squared y over denominator d x squared end fraction C o m i n g space b a c k space t o space t u r n i n g space p o i n t space o f space t h e space g r a p h comma space w h i c h space i s space g e n e r a l l y space k n o w n space a s space c r i t i c a l space p o i n t space a n d space d e n o t e d space b y space fraction numerator d y over denominator d x end fraction equals 0 A space f u n c t i o n space i s space s a i d space t o space b e space i n c r e a sin g space a t space a space p a r t i c u l a r space p o i n t space i f space fraction numerator d y over denominator d x end fraction a t space t h a t space p o i n t space i s space p o s i t i v e comma space s i m i l a r l y space f o r space d e c r e a sin g space i f fraction numerator d y over denominator d x end fraction a t space t h a t space p o i n t space i s space n e g a t i v e. space  A n space e x a m p l e space f o r space p o s i t i o n space v s space v e l o c i t y space a n d space p o s i t i o n space v s space a c c e l e r a t i o n space i s space g i v e n space a b o v e space i n space t h e space f o r m space o f space g r a p h. space y equals x squared space i s space g r a p h comma space w h e r e space x space i s space p o s i t i o n fraction numerator d y over denominator d x end fraction equals 2 x comma space p o s i t i o n space v s space v e l o c i t y comma space a space s t r a i g h t space l i n e space p a s sin g space t h r o u g h space o r g i n fraction numerator d squared y over denominator d x squared end fraction equals 2 comma space p o s i t i o n space v s space a c c e l e r a t i o n comma space a space s t r a i g h t space l i n e space p a s sin g space t h r o u g h space y equals 2

Answered by Vimala Ramamurthy | 18th Jul, 2014, 11:38: AM