Physics PDF: Distance and Displacement

travelled by a moving body cannot be zero but the fiaal d.rip,iacernent of a moving body can be zer{The displacement of a moving bodr-rrillbe zero if, after:::-.';jtag a certain distance, the moving boffinafly comes back to its starting poirt or starting position;. This rvill become clear from the f...

travelled by a moving body cannot be zero but the fiaal d.rip,iacernent of a moving body can be zer{The displacement of a moving bodr-rrillbe zero if, after:::-.';jtag a certain distance, the moving boffinafly comes back to its starting poirt or starting position;. This rvill become clear from the following examples. Suppose a man starts from piace -. and travels a distance of 5 km to reach place B the man travels fsee Figure i(o)]. fro* place B he travels another 3 km a::;. ::aches place C. And finally 4 km fiom piace C to reach back to the starting point -{ -... ! iure 5(a)]. In this case, though the man # 6r" distance hastravelledadistanceof5km+3km+4km=12kn-l.r*t.r:iraldisplacementofthemaniszero. This is because the man has reached back at the stari-:. :.,...1 and the straight line distance between the initial position A and final position A is zero..:*, :f ,,'e take a round trip and reach back at the starting point then, though we have travelled romo i:.:;r;., L-rnrr trinal displacement wilt be zero. This is because the straight line distance betrt-een ttre L:.r,'.' , ,:.rd nnal positions will be zero. For example, if we travel along a circular track of radius - :r,,- I::-., l:--'. :. -:. s.arting point A ---::*:t-rence of track) but [see Figure 5(bt], then though we have travelled a distance l:- ::.-: our final displacement will be zero. We will now solve a probie:: ::i: - : i-stance and displacement. CMIiliEN A man travels a distance of t.Sm tou-a:j: :',.; l,L-t tn tou'ards South and finally 4.5 m towards East. (,) What is the total distance travelled? (ll) What is his resultant displacement ? =8.0m (lr) To find the resultant displacement we shoui..:.i\r a map of the maris movements by choosing a convenient scale. Let 1 cnl ri:.resent 1 m. Then 1.5 m can be represented by 1.5 cm long line, 2.0 m br I r cm line and 4.5 m by a 4.5 cm long line. I We draw a 1.5 cm long line AB from West to East to represent 1.5 m towards East (see Figure 6). Then we draw a 2.0 cm long line BC towards South to represent 2.0 m towards South. And finally we draw a third line CD 4.5 cm long, towards East to represent a distance of l,- A------- -- 6 -asr ---rQFq 20m x--------U 4.5 m p East South -------Figure 6. Diagram for sample problem (Scale:1cm=1m) m towards East. Now, the resultant displacement can be iound by joining the starting point A with the finishing point D. Thus, the line AD represents the final displacement of the man. Let us measure the length of line AD. It is tor,Lnd to be 6.3 cm..1.5 Nou. lcrn:1m So, 6.1 cnr - 6.3 m Thus, the nnal displacement as represented by AD is 6.-l metres. Please note that whenever a bodv travels along a zig-zagpath, the final displacement is obtained by joining the starting point and the finishing point of the trody by a straight line. 12 Motion