38 CHAPTER 1 Kinematics: Motion in One Dimension X 21· .. Figure P1.21 shows a v

Question

38 CHAPTER 1 Kinematics: Motion in One Dimension X 21· .. Figure P1.21 shows a velocity-versus-time graph for the bicycle trips of two friends with respect to the parking lot where they started. (a) Determine their displacements in 20 s. (b) If Xena's position at time zero is 0 and Gabriele's position is 60 m, what time interval is needed for Xena to catch Gabri- ele? (c) Use the information from (b) to write function x(t) for Gabriele with respect to Xena. Figure P1.21 v (m/s) 10 ena Gabriele 4 0 .X 3 0 10 20 30 40 22·+/ Table 1.10 shows no si

Explanation / Answer

The speeds of the girls are:

vX=8 m/s

vG=6 m/s

If v=cnst, the movemenet is uniform. We'll have:

x(X)=vXt=160m

x(G)=vGt=120m

(b)

x(X)=vXt=8t

x(G)=60+vGt=60+6t

The condition to catch G is: x(X)=x(G) <--> t=60/[vX-vG]=30 s

(c) x(G/X)=(vX-vG)t=2t

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