At 20 seconds, the particle has a displacement of zero meters. It is at its star

Question

At 20 seconds, the particle has a displacement of zero meters. It is at its starting point wih trespect to north and south. However, it has travelled 100 meters.

How do I find out the value is 100 meters from the graph ? I don't understand that part.

Also, it says at 100 seconds, the particle has a positive, nonzero displacement. How is the displacement not zero if the velocity at 100 s is 0? v=d/t

FIGURE 1.7 Velocity vs. Time 30 20 20 30 40 50 60 70 80 90 1 10 20 30 J Time (s) displacement versus time If Figure 1.7 de h, the slope is velocity, and the only, and we desig is meaningless. On a veloc- about its motion

Explanation / Answer

Displacement is the shortest distance between initial and final position.

Distance travelled is the actual length of the path traversed.

On v-t graph, distance thavelled is shown by area under the graph.

or ,   Distance travelled at 20 s, D = Area (1-4) = Area(1-3) + Area(3-4)

                                                                  =(1/2)*(10- 0 )*10 + (1/2)*(2- 10 ) *10

                                                                  = 50 + 50 = 100 m

For discplacement from 0 to 2 s , we have accelearation , a = -20/20 = - 1 m/s2

u = 10 m/s ,   t = 20 - 0 = 20 s

displacement, s = ut + (1/2)at2 = 20*10 - 400/2 = 0

Area above time axis shows positive displacement and area below time axis shows negative displacement.

At t=100 s

Displacement, s = (Area above t-axi) - (Area below t-axis)

                        ={(1/2)*10*10} + {(1/2)*(80 - 55)*20} + {(3.14/4)*(100 - 80)2} - {(1/2)*((55-10)+(40-20))*10}

                        = 50 + 250 + 314 - 325

                        = 289 m   

or at t=100, s is +ve.

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