The equation of motion of a particle is given by The particle will come to rest at time

Question

The equation of motion of a particle is given by $x = a \sin (50 t + \frac{π}{3}) cm .$ The particle will come to rest at time $t_{1}$ and it will have zero acceleration at time $t_{2}$ . The $t_{1}$ and $t_{2}$ respectively are ______. [2026]

Smart Achievers · Accepted Answer

(1)

$Phase of the motion of particle is as follows:$

$v = 0, when particle cross A .$

$∴$ $t_{1} = \frac{π}{6 ω} = \frac{π}{300}$

$a = 0, when particle cross B .$

$∴$ $t_{2} = \frac{2 π}{3 ω} = \frac{π}{75}$

Solution

Q.
The equation of motion of a particle is given by $x = a \sin (50 t + \frac{π}{3}) cm .$ The particle will come to rest at time $t_{1}$ and it will have zero acceleration at time $t_{2}$ . The $t_{1}$ and $t_{2}$ respectively are ______. [2026]

1 $\frac{π}{300} s, \frac{π}{75} s$

2 $\frac{π}{75} s, \frac{π}{300} s$

3 $\frac{π}{300} s, \frac{π}{25} s$

4 $\frac{π}{50} s, \frac{π}{100} s$

Ans.
(1)

$Phase of the motion of particle is as follows:$

$v = 0, when particle cross A .$

$∴$ $t_{1} = \frac{π}{6 ω} = \frac{π}{300}$

$a = 0, when particle cross B .$

$∴$ $t_{2} = \frac{2 π}{3 ω} = \frac{π}{75}$

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Solution

Q. The equation of motion of a particle is given by x=asin(50t+π3) cm. The particle will come to rest at time t1 and it will have zero acceleration at time t2. The t1 and t2 respectively are ______. [2026]

1 π300s, π75s

2 π75s, π300s

3 π300s, π25s

4 π50s, π100s

Ans. (1) Phase of the motion of particle is as follows: v=0, when particle cross A. ∴ t1=π6ω=π300 a=0, when particle cross B. ∴ t2=2π3ω=π75