CALC? The coordinates of a bird flying in the xy-plane are given by x(t) = ?t and y(t) = 3.0 m - ?t2, where ? = 2.4 m/s and ? = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird as functions of time. (c) Calculate the magnitude and direction of the bird’s velocity and acceleration at t = 2.0 s. (d) Sketch the velocity and acceleration vectors at t = 2.0 s. At this instant, is the bird’s speed increasing, decreasing, or not changing? Is the bird turning? If so, in what direction?

Solution 7E Step 1: Provided, x(t) = t y(t) = 3.0 m - t 2 2 = 2.4 m/s and = 1.2 m/s Put t = 0 s, then, x(0) = 2.4 m/s × 0 s = 0 m y(0) = 3.0m - (1.2 m/s × 0 s ) = 3.0m Put, t = 1 s, then, x(1) = 2.4 m/s × 1 s = 2.4 m 2 2 y(1) = 3.0m - (1.2 m/s × 1 s ) = 1.8 m Put, t = 2 s, then, x(2) = 2.4 m/s × 2 s = 4.8 m y(1) = 3.0m - (1.2 m/s × 4 s ) = - 1.8 m a) We can plot the graph as mentioned below in figure 1. The vertical axis represents y (t) and the horizontal axis represents x(t). Figure 1