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shubham tomar Grade: 12
        


Is there something special when an object moves according to the law v=a*sqrt(s) ?


v -velocity
a-constant
s-displacement

actually, the acceleration for this type of motion comes out to be constant.
dv/dt=dv/ds*ds/dt
= [a/2*sqrt(s)]*a.sqrt(s)=a^2/2
can you intuitively explain why this happens ?

6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

v=ds/dt=Ksqrt(s)          (k=a^2/2)


  ds/sqrt(s)=kdt


  2sqrts=kt+c


 s=(kt+c)^2 /2


 it means graph between time and displacement is parabola......

6 years ago
Askiitians_Expert Yagyadutt
askIITians Faculty
74 Points
										

 Hiii shubham


 


 


v = a root(x)


 


dx/dt = a.root(x)


 


dx/a.root(x) = a.dt


Integrate it ...


 


2root(x) = a .t


 


or   x = a^2.t^2/4


 


x = kt^2


This is a parabolic path with respect to time..


d^2x/dt^2 = 2k  ( constant )


 


 


So this is just a projectile motion with object starting from rest...moved with constant acceleration 2k


 


Regards


Yagya


askiitians_expert

6 years ago
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