解答这个问题并尝试拓展讲解---Extraction Content:
Question Stem:
1. 一物体做直线运动,其加速度随时间变化的 a-t 图像如图所示。下列 v-t 图像中,可能正确描述此物体运动的是 ( )
Chart Description (a-t graph):
* Type: Line chart (specifically, piecewise constant function graph).
* Coordinate Axes:
* Horizontal axis: labeled 't', representing time. Starts at 0 and goes to the right. Marked points are T/2, T, 3T/2, 2T.
* Vertical axis: labeled 'a', representing acceleration. Origin is at 0. Positive direction is upwards, negative direction is downwards. Marked points are a0 and -a0.
* Data Series:
* From t=0 to t=T/2 (exclusive of T/2): The graph is a horizontal line segment at a = a0. Represented by a solid line from (0, a0) to (T/2, a0), with a dashed vertical line down at T/2.
* From t=T/2 to t=2T (inclusive of 2T): The graph is a horizontal line segment at a = -a0. Represented by a solid line from (T/2, -a0) to (2T, -a0). Dashed vertical lines are shown at T/2, 3T/2, and 2T extending to this horizontal line.
Options (v-t graphs):
The options are presented as four separate v-t graphs labeled A, B, C, and D. Each is a line chart showing velocity v as a function of time t.
Option A Chart Description:
* Type: Line chart (piecewise linear graph).
* Coordinate Axes:
* Horizontal axis: labeled 't'. Marked points are T/2, T, 3T/2, 2T. Starts at 0.
* Vertical axis: labeled 'v'. Marked points are v0, 0, -v0. Origin at 0.
* Data Series:
* Starts at (0, 0).
* Linear segment from (0, 0) to (T/2, -v0).
* Horizontal segment from (T/2, -v0) to (3T/2, -v0).
* Linear segment from (3T/2, -v0) to (2T, a value above 0, approximately v0/2).
Option B Chart Description:
* Type: Line chart (piecewise linear graph).
* Coordinate Axes:
* Horizontal axis: labeled 't'. Marked points are T/2, T, 3T/2, 2T. Starts at 0.
* Vertical axis: labeled 'v'. Marked points are v0, 0, -v0. Origin at 0.
* Data Series:
* Starts at (0, v0).
* Linear segment from (0, v0) to (T/2, 0).
* Horizontal segment from (T/2, 0) to (3T/2, 0).
* Linear segment from (3T/2, 0) to (2T, v0).
Option C Chart Description:
* Type: Line chart (piecewise linear graph).
* Coordinate Axes:
* Horizontal axis: labeled 't'. Marked points are T/2, T, 3T/2, 2T. Starts at 0.
* Vertical axis: labeled 'v'. Marked points are v0, 0, -v0. Origin at 0.
* Data Series:
* Starts at (0, 0).
* Linear segment from (0, 0) to (T/2, v0).
* Horizontal segment from (T/2, v0) to (T, v0).
* Linear segment from (T, v0) to (3T/2, 0).
* Linear segment from (3T/2, 0) to (2T, -v0).
Option D Chart Description:
* Type: Line chart (piecewise linear graph).
* Coordinate Axes:
* Horizontal axis: labeled 't'. Marked points are T/2, T, 3T/2, 2T. Starts at 0.
* Vertical axis: labeled 'v'. Marked points are v0, 0, -v0. Origin at 0.
* Data Series:
* Starts at (0, 0).
* Linear segment from (0, 0) to (T/2, v0).
* Horizontal segment from (T/2, v0) to (T, v0).
* Linear segment from (T, v0) to (2T, -v0). (The point at 3T/2 is on this segment, where v=0).