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Question

# A point moves on the x−y plane according to the law x=asinωt and y=a(1−cosωt) where a and ω are positive constants and t is in seconds. Find the distance covered in time t0.

A
aωt0
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B
2a2+2a2cosωt0
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C
2asinωt02
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D
2acosωt02
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Solution

## The correct option is A aωt0Position vector of the point →r=asinwt^i+a(1−coswt)^jVelocity vector →v=→drdt=awcoswt^i+awsinwt^jDistance covered in time to by the point is the integral of speed or magnitude of velocity vector =∫t00|→v|dt=∫t00√(awcoswt)2+(awsinwt)2dt=∫t00awdt=awto

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