# Formula for Power from Kinetic Energy

Work Done = $$Fd$$

Power = $$Fv$$

If the (net) Work Done = Change in Kinetic Energy, and the object starts from rest:
Work Done = $$\frac{1}{2} mv^2$$

Power = $$\frac{1}{2} m av$$

Power = $$\frac{1}{2} F v$$

This isn't correct though. How do I remove factor of $$\frac{1}{2}$$?

Then $$W = \frac{1}{2} mv^2$$
Then, since power is $$P= \frac{dW}{dt}$$ we have that
$$P = \frac{dW}{dt} = \frac{1}{2} m \frac{d}{dt} v^2 = mv \dot{v} = (ma)v = F\cdot v$$
{"ft_lang_label":"__label__en","ft_lang_prob":0.8130142,"math_prob":1.00001,"size":265,"snap":"2021-04-2021-17","text_gpt3_token_len":91,"char_repetition_ratio":0.18390805,"word_repetition_ratio":0.0,"special_character_ratio":0.38867924,"punctuation_ratio":0.071428575,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.00001,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-19T21:23:52Z\",\"WARC-Record-ID\":\"<urn:uuid:a09ed390-4264-4601-a013-ef7c2bfec0af>\",\"Content-Length\":\"146464\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c0d088c1-b518-48d3-bf00-71023245f707>\",\"WARC-Concurrent-To\":\"<urn:uuid:3ac25c3c-9a7d-4028-ace7-bcb017a06def>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/451101/formula-for-power-from-kinetic-energy\",\"WARC-Payload-Digest\":\"sha1:I2FUNXSRXHBIWJHLFUNPDZTHQ4LQXZGV\",\"WARC-Block-Digest\":\"sha1:35EX452SWIQXHK3ZZSFFIP45H64RNZXS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703519784.35_warc_CC-MAIN-20210119201033-20210119231033-00137.warc.gz\"}"}