A particle is executing SHM about y=0 along y-axis. Its position … - Vidyadip

MCQ

A particle is executing $SHM$ about $y=0$ along $y$-axis. Its position at an instant is given by $y=(7 \,m )$ sin( $\pi f)$. Its average velocity for a time interval $0$ to $0.5 \,s$ is ........... $m / s$

✓
$14$
B
$7$
C
$\frac{1}{7}$
D
$28$

✓

Answer

Correct option: A.

$14$

a
(a)

Average velocity, $v_{\text {avg }}=\frac{\text { displacement }}{\text { total time }}$

Given, $y=7 \sin (\pi t) m , t=0$ to $0.5$

$y$ at $t=0, x_1=7 \sin \left(0^{\circ}\right)=0$

$y$ at $t=0.5$,

$x_2=7 \sin (\pi / 2)=7$

$\therefore V_{\text {avg }}=\frac{7-0}{0.5-0}=14$

$v_{\text {avg }}=14 m / s$

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