Question

A particle moves in xy plane according to the law x=4sin6t and y=4 (1-cos6t).the distance traversed by the particle in 4s is

Answer 1

Final Result : 96 units

Velocity in x - direction :
$\frac{dx}{dt} = 4 \times 6 \cos(6t) \\ v(x) = 24 \cos(6t) - - - - (1) \\ \\velocity \: in \: y \: direction \\ \frac{dy}{dt} = 24 \sin((6t) \\ v(y) = 24 \sin(6t)$
$speed \: of \: particle \: is \: given \: as \: \\ \sqrt{ {v(x)}^{2} + {v(y)}^{2} } = 24 \: \: units \:$

Distance traversed by the particle = Speed * time = 24 * 4 = 96 units

Hope you understand my answer :

Answer 2

Step-by-step explanation:

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