Question

A particle moves along the x-axis according to $x=A[1+\sin \omega t]$. What distance does is travel in time interval from t=0 to $t=2.5\pi /\omega$?

• A. 4 A
• B. 6 A
• C. 5 A
• D. 3 A

Answer 1

Answer: (C)

5 A

$t=\frac{2.5\pi }{\omega }=\frac{2.5\pi }{\left(2\pi /T\right)}=\left(2.5\right)\left(\frac{T}{2}\right)$
$=5\left(\frac{T}{4}\right)$
Partieie starts from extreme position and in every $\frac{T}{4}$ time it travels a distance A. So in time t=5(T/4) it will travel a distance 5A.