Show that the displacement in time t is ...

Show that the displacement in time t is proportional to `t^((3)/(2))` under the influence of a constant power.

Text Solution

Verified by Experts

`P=Fv=mav=(mv^(2))/(t)=(m)/(t)(2as)`
i.e. `s=(Pt)/(2ma)=(pt^(3))/(4ms)`
hence `s^(2)=(pt^(3))/(4m)ors=(1)/(2)sqrt((P)/(m)).t^((3)/(2))" i.e. "spropt^((3)/(2))`.

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If the displacement s at a time t is given by s = sqrt(1-t) , than the velocity is

directly proportional to displacement

inversely proportional to displacement

equal to displacement

None of these

A body executes S.H.M. under the influence of one force and has a period T_(1) second and the same body executes S.H.M. with period T_(2) second when under the influence of another force. When both forces act simultaneously and in the same direction, then the time period of the same body is :

`(T_(1)+T_(2))s`

`sqrt(T_(1)^(2)+T_(2)^(2))s`

`sqrt((T_(1)^(2)+T_(2)^(2))/(T_(1)T_(2)))s`

`sqrt((T_(1)^(2)T_(2)^(2))/((T_(1)^(2)+T_(2)^(2)))s`.

The displacement of a particle moving in one dimension under the action of a constant force is related to timer by the equation t= sqrt(x + 3) , where x is in metres and in second. What is the displacement of particle when its velocity is zero?

zero

1 m

2 m

3 m