Four successive displacements of a particle moving along a straight track are x1,x2,x3 and x4. Displacements directed towards the right are taken as positive while those towards the left are negative.
(a) Derive, in symbols, an expression for the net displacement of the particle after the four moves.
(b) Express, again in symbols, the total distance travelled for the same four moves.
(c) Hence or otherwise, show that the total distance travelled is always greater than or equal to the magnitude of the net displacement, i.e., distance≥∣displacement∣.
(d) Using x1=+12m,x2=−15m,x3=+9m,x4=−4m, verify numerically the result obtained in part (c).