Question

۴۲- با توجه به شکل زیر توضیح دهید کدام یک از نمودارهای مکان - زمان (الف) یا (ب) می تواند نشان دهنده نمودار مکان - زمان یک متحرک باشد.

Explanation:

Analyze graph (a)

$$ \forall t \ge 0, \quad |\{x \mid (t, x) \in \text{graph (a)}\}| \le 1 $$

Analyze graph (b)

$$ \exists t_0 > 0 \quad \text{such that} \quad |\{x \mid (t_0, x) \in \text{graph (b)}\}| = 2 $$

Determine physical possibility

$$ \text{A moving object cannot occupy two different positions } x_1 e x_2 \text{ at the same instant } t_0. $$

Answer:

Graph (a) can represent the position-time graph of a moving object.

In graph (b), drawing a vertical line at certain times intersects the curve at two points, meaning the object would have to be at two different positions at the exact same instant, which is physically impossible.