The distance x covered by a body moving in a straight line in time t is given by the relation-

2x²+3x=t

If v is the velocity of body at a certain instance of time, find it's acceleration.

Asked by simasarkar1968 | 28th May, 2020, 07:02: PM

Expert Answer:

Distance is x 
and time is t 
The equation given is 
t = 2x²+3x
 
W e space k n o w comma space
v space equals space fraction numerator d x over denominator d t end fraction space... space left parenthesis 2 right parenthesis space
a space equals fraction numerator d v over denominator d t end fraction equals fraction numerator d over denominator d t end fraction open parentheses fraction numerator d x over denominator d t end fraction close parentheses equals space fraction numerator d squared x over denominator d t squared end fraction space... space left parenthesis 3 right parenthesis
w h e r e comma space v space i s space v e l o c i t y space

L e t apostrophe s space d i f f e r e n t i a t e space e q u a t i o n space left parenthesis 1 right parenthesis space w. r. t space t i m e comma
w e space g e t comma space
1 space equals space open parentheses 4 x plus 3 close parentheses space fraction numerator d x over denominator d t end fraction space
H e n c e comma space
1 space equals space space open parentheses 4 x plus 3 close parentheses space v space
1 over v space equals space space open parentheses 4 x plus 3 close parentheses space... space left parenthesis 4 right parenthesis thin space space
D i f f e r e n t i a t i n g space e q space left parenthesis 4 right parenthesis space a g a i n space w. r. t space t i m e comma space w e space g e t comma space
open parentheses fraction numerator negative 1 over denominator v squared end fraction close parentheses fraction numerator d v over denominator d t end fraction space equals space 4 space open parentheses fraction numerator d x over denominator d t end fraction close parentheses
T h u s comma space

open parentheses fraction numerator negative 1 over denominator v squared end fraction close parentheses a space equals space 4 space v space left parenthesis f r o m space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis right parenthesis space
rightwards double arrow A c c e l e r a t i o n comma space space a space equals space minus 4 v cubed space

Answered by Shiwani Sawant | 28th May, 2020, 08:46: PM

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