The equation of motion of a particle starting at t = 0 is given by x = 5sin(20t+ (π/3)) where x is in centimeter and t is in second. When does the particle come to rest for the second time?

Question

The equation of motion of a particle starting at t = 0 is given by x = 5sin(20t+ (π/3)) where x is in centimeter and t is in second. When does the particle come to rest for the second time? (A)  (π/10)s (B)  (7 π/100)s (C)  (7 π/120)s (D)  (5 π/7)s

Tardigrade Admin · Accepted Answer

v = 100 cos (20t + (π/3)) = 0 For the second time, 20 t + (π/3) = (3π/2) t = (7π /120) second

Q. The equation of motion of a particle starting at $t = 0$ is given by $x = 5 s in (20 t + \frac{π}{3})$ where $x$ is in centimeter and t is in second. When does the particle come to rest for the second time?

$\frac{π}{10} s$

$\frac{7 π}{100} s$

$\frac{7 π}{120} s$

$\frac{5 π}{7} s$

$v = 100 cos (20 t + \frac{π}{3}) = 0$
For the second time, $20 t + \frac{π}{3} = \frac{3 π}{2}$
$t = \frac{7 π}{120} seco n d$

Q. The equation of motion of a particle starting at t=0 is given by x=5sin(20t+3π​) where x is in centimeter and t is in second. When does the particle come to rest for the second time?

10π​s

1007π​s

1207π​s

75π​s