A particle starts moving at t = 0 with its position given by the equation x = 5 (20 t + /3) , where x is in centimetre and t is in second. Determine the time when the particle first comes to rest.

Step-by-step solution

Given the position of the particle as x = 5 (20t + 3 ) . The velocity of the particle is the rate of change of position with respect to time: v = dx dt = d dt [ 5 (20t + 3 ) ] v = 100 (20t + 3 ) The particle comes to rest when its velocity becomes zero. Thus, v = 0 . 100 (20t + 3 ) = 0 (20t + 3 ) = 0 For the first time the particle comes to rest, the phase angle must be equal to 2 . 20t + 3 = 2 20t = 2 - 3 20t = 6 t = 120 s