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Question

A point moves in x-y plane according to the law x=4 sin 6t and y=4(1-cos 6t). The distance traversed by the particle in 4 seconds is (x and y are in meters)


A

96 m

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B

48 m

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C

24 m

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D

108 m

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Solution

The correct option is A

96 m


x=4 sin 6t; y=4(1-cos 6t)
dxdt=vx=4.6 cos 6t; dydt=vy=4.6 sin 6t
Now speed = |v|=v2x+v2y
=(24 cos 6t)2+(24 sin 6t)2
Speed = 24 m/s
Oh wow!
Speed is constant through the journey
So now it's easy
I know speed = distancetime
24=distance4
Distance = 96 m


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