The equation of motion of a particle is given by x = a (50t + 3 ) 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 _______.

Step-by-step solution

The equation of motion is given by x = a (50t + 3 ) . Velocity is the rate of change of displacement: v = dx dt = 50a (50t + 3 ) The particle comes to rest when v = 0 . For the first time it comes to rest: (50t₁ + 3 ) = 0 50t₁ + 3 = 2 50t₁ = 2 - 3 = 6 t₁ = 300 s Acceleration is the rate of change of velocity: A = dv dt = -2500a (50t + 3 ) The particle has zero acceleration when A = 0 . For the first time it has zero acceleration: (50t₂ + 3 ) = 0 50t₂ + 3 = 50t₂ = - 3 = 2 3 t₂ = 2 150 = 75 s Answer: 300 , s, 75 , s