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. Graph of 1/V vs x for a particle under rectilinear motion is as shown, where V is velocity and x is position. The time taken by particle to move from x = 4 m to x = 12 m is

. Graph of 1/V vs x for a particle under rectilinear motion is as shown, where V is velocity and x is position. The time taken by particle to move from x = 4 m to x = 12 m is

Question Image
Grade:11

1 Answers

Vikas TU
14149 Points
2 years ago
Dear student 
 
Let y=1/v
then equation of straight line in y-x graph in two-point form is 
 
y-1/2 =(2-1/2)/(12-4)(x-4)
gives y=(3x-4)/16 +1/2
or
1/v=(3x-4)/16+1/2 = (3x-4)/16
or 
v=16/(3x-4)
or
dx/dt=16/(3x-4)
or
(3x-4)dx=16dt
or
(3/2)x^2 – x/4 =16 t
 
t=(3x^2/32)-x/4
let when x=4 t=t1 and at x=12 t=t2
then 
t1=1/2 and t2=21/2
so t2-t1 = 10sec

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