A particle is oscillating according to the equation V(t) = 4 sin 0.4π t metres. In how much time after the motion begins will that particle reach the extreme position from the mean position?

Question

A particle is oscillating according to the equation V(t) = 4 sin 0.4π t metres. In how much time after the motion begins will that particle reach the extreme position from the mean position? (A)  1.25 s  (B)  3.25 s  (C)  4.25 s  (D)  2.25 s

Tardigrade Admin · Accepted Answer

From the given equation, ω=(2π/T)=0.4π T=(2π/ω) =(2π/0.4π)=5s Time taken to reach extreme position from mean position =(1/4) T (5/4)=1.25 s

Q. A particle is oscillating according to the equation $V (t) = 4 s in 0.4 π t$ metres. In how much time after the motion begins will that particle reach the extreme position from the mean position?

$1.25 s$

$3.25 s$

$4.25 s$

$2.25 s$

From the given equation, $ω = \frac{2 π}{T} = 0.4 π$
$T = \frac{2 π}{ω}$
$= \frac{2 π}{0.4 π} = 5 s$
Time taken to reach extreme position from mean position
$= \frac{1}{4} T$
$\frac{5}{4} = 1.25 s$

Q. A particle is oscillating according to the equation V(t)=4sin0.4πt metres. In how much time after the motion begins will that particle reach the extreme position from the mean position?

1.25s

3.25s

4.25s

2.25s