IIT JEE , AIEEE Forum - Physics , Mechanics

sneha_91

the law of motion of the body along a straight line is x=vt/2,x and v are displacement and velocity of the body at a time t.show that the body moves under constant acceleration

iitkgp_bipin

x = vt/2

We know : v = dx/dt

x = (dx/dt).t/2

2dt/t = dx/x

Integrating both the sides :

2lnt + c = lnx (where c is the constant of integration)

ln(e^c.t²) = ln(x)

x = e^c.t²

dx/dt = e^c.(2t)

acceleration = d²x/dt² = d(dx/dt)/dt = d{e^c.(2t)}/dt = 2e^c (a constant)

Hence acceleration is constant.

sneha_91

can u explain it without integrating both sides.....in simple terms please

angelh

for expert
2Int+c=Inx
understood till here how does next step comes

phyana

hey sneha
approach this question in another way.
the equation u have written can be written as
(x / t) = ( v / 2)
this is the simplified form of the famous equation--
(total displacement / total time) = average velocity
average velocity=(initial velcity+final velocty) / 2
final velocity = v
initial velocity =u=0
the equation is derived ont the basis tha movement is under const acc.
so being in this form the motion is under constant accelaration.
lrate mw plzzzzzzzzzzzzzz

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