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Question

What is the distance travelled by a point during the time t. if it moves in X-Y plane according to relation.
X=asinωt
Y=a(1cosωt)

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Solution

Given that,

x=asinωt.....(I)

y=a(1cosωt)

y=aacosωt.....(II)

Now, the velocity for x

On differentiate of equation (I)

vx=dxdt

vx=aωcosωt

Now again differentiate of equation (II)

The velocity for y

vy=dydt

vy=aωsinωt

Now the velocity is

v=v2x+v2y

v=a2ω2(sin2ωt+cos2ωt)

v=aω

Now, the distance travelled in time t

D=v×t

D=aωt

Hence, the distance travelled by a point during the time t is aωt


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