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if a=2x; initally particle is at x=2m and is moving with 3m/s then find out v at x=5m 

Asked by gargpuneet989 25th June 2018, 5:45 PM
Answered by Expert
Answer:
Given acceleration a(x) = 2x is function of position.
 
let us integrate acceleration a(x) from x=2 to x=5, begin mathsize 12px style integral subscript 2 superscript 5 2 x space d x space equals space 21 end style J/kg....................(1)
Eqn(1) can be viewed as Workdone on a unit mass by a variable force from x=2  to x=5 .
 
Workdone will change the kinetic energy. Hence begin mathsize 12px style 1 half open parentheses v subscript f superscript 2 space minus space v subscript i superscript 2 close parentheses space equals space 21 end style J/kg  .............(2)
where vf is final velocity at x=5 and vi is initial velocity at x=2. Unit mass is assumed in eqn.(2)
 
By substituting vi = 3 m/s in eqn(2), we get  begin mathsize 12px style v subscript f space equals space square root of 51 space m divided by s space space equals space 7.14 space m divided by s end style
Answered by Expert 25th June 2018, 10:48 PM
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