# Infer maximum covered distance

1. Sep 28, 2008

### 12monkey

Hi everyone, I have one simple question.
Let's assume that a character is moving in an environment and it can be simulated as a particle with mass =1. Several forces acted upon the character, making the character to move. In other words, the sum of the forces F equals the acceleration of the character. In addition, at any time the character is subjected to some kinematic constraints. In particlular, its velocity v can not exceed a maximum value Vmax (||v|| < Vmax) and its acceleration can not exceed a maximum value i.e. ||F||<Amax. Can we say that the maximum distance that the character can travel for a given time step Dt is Vmax*Dt?

2. Sep 28, 2008

Yes, we can.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.894295334815979, "perplexity": 752.0053793619039}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745486.91/warc/CC-MAIN-20181119064334-20181119090334-00175.warc.gz"}