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A Numerical from Kinematics

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Advait Asks:

“A test projectile is fired horizontally into a viscous liquid with a velocity u.The retarding force is propotional to the square of the velocity, so that the acceleration becomes a=-k(v)^2 .v is the velocity at that point. Derive expressions for the distance D travelled in the liquid and corresponding time t required to reduce the velocity to u/2.
Neglect any vertical  motion”


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