A particle begins its motion at t = 0 according to the equation x = 5 (20 t + /3) , where x is in centimetre and t is in second. At what time will the particle first have zero acceleration?

Step-by-step solution

The equation of motion of the particle is given by: x = 5 (20 t + 3 ) The velocity v is the first derivative of displacement with respect to time: v = dx dt = 100 (20 t + 3 ) The acceleration a is the first derivative of velocity with respect to time: a = dv dt = -2000 (20 t + 3 ) For the acceleration to be zero, we must have: -2000 (20 t + 3 ) = 0 (20 t + 3 ) = 0 This implies that the phase must be an integer multiple of . Since we need the first time t > 0 when acceleration is zero, we equate the phase to the nex