A particle starts at rest, first makes a period of uniform acceleration linear motion with the acceleration A1 & nbsp; for a period of time, then makes a uniform deceleration linear motion with the acceleration A2 until it stops. The total time of the particle motion is t, and the total displacement of the particle is calculated

A particle starts at rest, first makes a period of uniform acceleration linear motion with the acceleration A1 & nbsp; for a period of time, then makes a uniform deceleration linear motion with the acceleration A2 until it stops. The total time of the particle motion is t, and the total displacement of the particle is calculated

Let the maximum velocity in motion be VM, then the total time t = VMA1 + vma2 & nbsp; & nbsp; & nbsp; ① then the total displacement x = vm2t1 + vm2t2 = vm2t & nbsp; & nbsp; & nbsp; ② simultaneous solution of the two equations gives x = a1a2t22 (a1 + A2). Answer: the total displacement of the particle is x = a1a2t22 (a1 + A2)