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:-

Options

A. `a^(2)y+bx^(2)=0`
B. `a^(2)y=bx^(2)`
C. `y=b/a^(2)`
D. `ay^(2)=b^(2)x`

Answer

A

Explanation

`x=at, y=-bt^(2) rArr a^(2)y+bx^(2)=0`