Question

The velocity of particle is given by v = (3î + 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
pls give answer with full explanation.​

Answer 1

Answer:

given = v = (3î + 6tj) m/s,

to find =  y =?  i.e equation of trajectory.

solution :-

V = 3i + 6tJ

Vy = 6t

dy/dt = 6t

dy =  6tdt

integrated on the 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

Answer 2

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