The position of a particle is: x = a sin(50t + π/3). If the speed and acceleration become zero for the first time at t₁ and t₂ respectively, find t₁ and t₂.

Question

The position of a particle is: x = a sin(50t + &pi;/3). If the speed and acceleration become zero for the first time at t₁ and t₂ respectively, find t₁ and t₂.

Shiksha Nation · Accepted Answer

Given:
x = a sin(50t + &pi;/3)
Velocity:
v = dx/dt
= 50a cos(50t + &pi;/3)
For velocity to be zero:
cos(50t + &pi;/3) = 0
50t + &pi;/3 = &pi;/2
50t = &pi;/6
t₁ = &pi;/300
Acceleration:
a = &minus;&omega;&sup2;x
Acceleration becomes zero when:
x = 0
sin(50t + &pi;/3) = 0
50t + &pi;/3 = &pi;
50t = 2&pi;/3
t₂ = &pi;/75
Final Answer
t₁ = &pi;/300 sec
t₂ = &pi;/75 sec

The position of a particle is: x = a sin(50t + π/3). If the speed and acceleration become zero for the first time at t₁ and t₂ respectively, find t₁ and t₂.

Verified Answer

Final Answer