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A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v = x a . The displacement of the particle varies with time as ?

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v = x a . The displacement of the particle varies with time as ?

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
v = ax
\frac{dx}{dt} = ax
\frac{dx}{x} = adt
\int \frac{dx}{x} = a\int dt
lnx = at + c
\Rightarrow x = e^{at+c}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
Shivam
13 Points
2 years ago
V=a√xdx/dt =a√xdx/√x=adtIntegrating both sides we get,,2√x= at+cSo, x becomes directly proportional to t^2

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