Question

A point moves in ` x-y` plane according to the law ` x= 4 sin 6 t ` and ` y= 4 ( 1- cos 6 t)`. Fimd distance traversed by the particle in ` 5 seconds`, when (x0 and (y) are in metres.

Answer 1

` V-x = (dx)/(dT) = 4 xx 6 sin cos 6 t` or ` t = 24 cos 6 t` ltbRgt ` v_y = (dy)/(dt) =4 xx 6 sin 6 t= 24 cos 6 t` ltBrgt :. Velocity, ` v = sqrt (v_x^2 +v_y^2)`
` =sqrt( ( 24 cos 6 t) ^2 + (24 sin 6 t )^2 ) = 24 ms^(-2)`. ltbRgt It means, velcity of point is constanct. The distance travelled by particle in ` 5 sec`
` = 24 xx 5 = 120 m`.