a particle moves along the x-axis according to the equation x=A sin(wt) find out the distance travelled by the particle during the time interval t=0 to t=t

Dear Student,

Please find below the solution to the asked query:

The displacement of the particle at any moment is given by the equation,

$x=A \sin \omega t$

But the distance travelled will be having different values,

If the 0<t<T/4, the distance travelled by the particle is $x=A \sin \omega t$.

If T/4 < t < T/2, the distance travelled by the particle is $x\text{'}=A+A \sin \omega t$

If T/2 < t < 3T/4, the distance travelled by the particle is $x\text{'}\text{'}=2A+A \sin \omega t$

So, in this manner for every T/4 time interval, the distance travelled increases by A.

Hope this information will clear your doubts about the topic.

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