Question

The table gives coordinates of a particle moving through space along a smooth curve. 0 2.8 9.6 3.8 0.5 3.7 7.5 3.4 1.0 4.1 6.0 3.0 1.5 5.1 6.8 2.9 2.0 7.6 7.4 2.6 (a) Find the average velocities over the time intervals [0, 1], [0.5, 1], [1, 2], and [1, 1.5]. (Round your answers to the nearest tenth.) [0.5, 1: Vave - [1, 2] Vave [1,15% [1, 1.5]: Vave vave- (b) Estimate the velocity and speed of the particle at t 1. (Use the time intervals [0.5, 1] and [1, 1.5] to calculate your answer. Round the speed to two decimal places.)

Answer 1

at t = 0, the prostate position of (2.8, 9.6, 3.8) We know, Average velocity = displacement/total time thus (a) [0, 1] leftarrow time interval, v_are = squareroot (1.1 - 2.8)^2 + (6 - 9.6)^2 + (3 - 3.8)^2/1 v_are = squareroot 1.69 + 12.96 + 0.67 = 3.91 unit [0.51, 1]: v_are = squareroot (4.1 - 3.7)^2 + (6 - 7.5)^2 + (3 - 3.4)^2/0.5 v_are = 3.2 unit [1, 2]: v_are = squareroot (7.6 - 4.1)^2 + (7.4 - 6)^2 + (2.6 - 3)^2/9 v_are = 3.79 unit [1, 1.5]: v)are = squareroot (5.1 - 4.1)^2 + (6.8 - 6)^2 + (2.9 - 3)^2/0.5 v_are = 2.57 unit (b) time interval [0.5, 1] distance travel, squareroot (4.1 - 9.7)^2 + (6 - 7.5)^2 + (3 - 3.4)^2 = 4.6 unit final interval [1, 1.5], distance travel = squareroot (5.1 - 4.1)^2 + (6.8 - 6)^2 + (2.9 - 3)^2 = 1.285 unit Therefore Total final travel