F9 for recalculate.

σ_t = 0.198 (slider from 0.001 to 0.5, step 0.001)
n = 99 (slider from 10 to 200, step 1)
intervals = Sequence(RandomNormal[1, σ_t], k, 1, n)
σ_v = 0.201 (slider from 0.001 to 0.5, step 0.001)
t = 0 (slider from 0 to n, step 0.1)
times = Sequence(Sum[intervals, k], k, 1, n)
thetas = Sequence(RandomUniform[0, 6.28319], k, 1, n)
distances: (intervals * Sequence[RandomNormal[1, σ_v], k, 1, n])
directions = Sequence({cos(Element[thetas, i]), sin(Element[thetas, i])}, i, 1, n)
moves = Join({{{0, 0}}, (distances * directions)})
movesX = Sequence(Element[Element[moves, k], 1], k, 1, n)
movesY = Sequence(Element[Element[moves, k], 2], k, 1, n)
positions = Sequence((Sum[movesX, k], Sum[movesY, k]), k, 1, n)
O = (0, 0)
pos = IndexOf(0, floor(times - t))
trail = If(Element[times, n] > t, PolyLine[Take[positions, 1, pos]], PolyLine[positions])
list1 = Last(times)