Chapter 2, Problem 2P

|| A person is walking briskly in a straight line, which we shall call the x axis. Figure 2.42 shows a graph of the person’s position x along this axis as a function of time t. (a) What is the person’s displacement during each of the following time intervals: (i) between t = 1.0 s and t = 10.0 s, (ii) between t = 3.0 s and t = 10.0 s, (iii) between t = 2.0 s and t = 3.0 s, and (iv) between t = 2.0 s and t = 4.0 s? (b) What distance did the person move from (i) t = 0 s to t = 4.0 s, (ii) t = 2.0 s to t = 4.0 s, and (iii) t = 8.0 s to t = 10.0 s?

Figure 2.42

Problem 2

2.2. Set Up: From the graph the position x_t at each time t is: x₁ = 1.0 m, x₂ = 0, x₃ = −1.0 m, x₄ = 0, x₈ = 6.0 m, and x₀ = 6.0 m.

Solve (a) The displacement is Δx. (i) Δx = x₁₀ − x₁ = +5.0 m; (ii) Δx = x₁₀ − x₃ = +7.0 m; (iii) Δx = x₃ − x₂ = −1.0 m; (iv) Δx = x₄ − x₂ = 0

(b) (i) 3.0 m + 1.0 m = 4.0 m; 90° (ii) 1.0 m + 1.0 m = 2.0 m; (iii) zero (stays at x = 6.0 m)