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Path traced by a moving particle in spac...

Path traced by a moving particle in space is called trajectory of the particle. Shape of trajectiry is decided by the forces acting on the particle. When a coordinate system is associated with a particle motion, the curve equation in which the particle moves `[y=f(x)]` is called equation of trajectory. It is just giving us the relation among x and y coordinates of the particle i.e. the locus of particle. To find equation of trajectory of a particle, find first x and y coordinates of the particle as a function of time eliminate the time factor.
The position vector of car w.r.t. its starting point is given as `vec(r)=at hat(i)- bt^(2) hat(j)` where a and b are positive constants. The locus of a particle is:-

A

`a^(2)y+bx^(2)=0`

B

`a^(2)y=bx^(2)`

C

`y=b/a^(2)`

D

`ay^(2)=b^(2)x`

Text Solution

Verified by Experts

The correct Answer is:
A
`x=at, y=-bt^(2) rArr a^(2)y+bx^(2)=0`
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Path traced by a moving particle in space is called trajectory of the particle. Shape of trajectiry is decided by the forces acting on the particle. When a coordinate system is associated with a particle motion, the curve equation in which the particle moves [y=f(x)] is called equation of trajectory. It is just giving us the relation among x and y coordinates of the particle i.e. the locus of particle. To find equation of trajectory of a particle, find first x and y coordinates of the particle as a function of time eliminate the time factor. In above the velocity (i.e. (dvec(r))/(dt)) at t=0 is :-

Path traced by a moving particle in space is called trajectory of the particle. Shape of trajectiry is decided by the forces acting on the particle. When a coordinate system is associated with a particle motion, the curve equation in which the particle moves [y=f(x)] is called equation of trajectory. It is just giving us the relation among x and y coordinates of the particle i.e. the locus of particle. To find equation of trajectory of a particle, find first x and y coordinates of the particle as a function of time eliminate the time factor. In above question initial acceleration (i.e. (d^(2)vec(r))/(dt^(2))) of particle is :-

Knowledge Check

  • If the external force acting on a system of particle is zero then …………..

    A
    `vec(a)_(cm)=0`
    B
    `vec(v)_(cm)=0`
    C
    `vec(r )_(cm)=0`
    D
    `vecp=0`

  • The equation of motion of a particle is x= a cos (alpha t)^(2) . The motion is………..

    A
    periodic but not oscillatory
    B
    periodic and oscillatory
    C
    oscillatory but not periodic
    D
    neither periodic nor oscillatory

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