Question

The velocity of particle is given by v = (3i +6tj) m/s, where t is time in second, the equation of trajectory of
particle is [Assume, particle starts from origin]
(1) y = x²/3
(2) y = x²/9
(3) y = 2x²/9
(4) y = x²/16​

Answer 1

y=x2

Explanation:

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Answer 2

Given:

v = (3î + 6tj) m/s,

Find:

y = ?  

i.e equation of trajectory.

solution :-

V = 3i + 6tJ

Vy = 6t

dy/dt = 6t

dy =  6tdt

integrated on both sides,

∫dy = ∫6tdt

y = 6t²/2 + c

y = 3x²/q

y  = x² / 3  

now, Vx = 3

 dx / dt = 3

    dx = 3dt  

    ∫dx = ∫3dt

       x = 3t +c

     t = 0 , c = 0

     t = x / 3

      y = x² / 3

Hence, The velocity of the particle is given by v = (3i +6tj) m/s, where t is time in second, the equation of trajectory of  particle is y = x²/3.