{"id":265793,"date":"2022-09-10T13:29:54","date_gmt":"2022-09-10T07:59:54","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-of-mass-m-is-driven-by-a-machine-that-delivers-a-constant-power-k-watts-if-the-particle-starts-from-rest-the-force-on-the-particle-at-time-t-is-2\/"},"modified":"2022-09-10T13:29:54","modified_gmt":"2022-09-10T07:59:54","slug":"a-particle-of-mass-m-is-driven-by-a-machine-that-delivers-a-constant-power-k-watts-if-the-particle-starts-from-rest-the-force-on-the-particle-at-time-t-is-2","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-mass-m-is-driven-by-a-machine-that-delivers-a\/","title":{"rendered":"A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is :"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is :","custom_permalink":"question\/physics\/a-particle-of-mass-m-is-driven-by-a-machine-that-delivers-a\/"},"categories":[],"acf":{"question":"<p>A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is :<\/p>","options":[{"option":"<p><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><msqrt><mi>mk<\/mi><\/msqrt><msup><mi mathvariant=\"normal\">t<\/mi><mrow><mo>\u2212<\/mo><mn>1<\/mn><mo>\/<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/math><\/p>","correct":false},{"option":"<p><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><msqrt><mn>2<\/mn><mi>mk<\/mi><\/msqrt><msup><mi mathvariant=\"normal\">t<\/mi><mrow><mo>\u2212<\/mo><mn>1<\/mn><mo>\/<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/math><\/p>","correct":false},{"option":"<p><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><msqrt><mi>mk<\/mi><\/msqrt><msup><mi mathvariant=\"normal\">t<\/mi><mrow><mo>\u2212<\/mo><mn>1<\/mn><mo>\/<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/math><\/p>","correct":false},{"option":"<p><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><msqrt><mfrac><mi>mk<\/mi><mn>2<\/mn><\/mfrac><\/msqrt><msup><mi mathvariant=\"normal\">t<\/mi><mrow><mo>\u2212<\/mo><mn>1<\/mn><mo>\/<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/math><\/p>","correct":true}],"solution":"<p>P = Fv = mav<br><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><mo stretchy=\"false\">\u21d2<\/mo><mi mathvariant=\"normal\">K<\/mi><mo>=<\/mo><mi>mv<\/mi><mfrac><mi>dv<\/mi><mi>dt<\/mi><\/mfrac><\/mrow><\/mstyle><\/math><br>By integrating the equation<br><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><mo stretchy=\"false\">\u21d2<\/mo><mo>\u222b<\/mo><mi>vdv<\/mi><mo>=<\/mo><mo>\u222b<\/mo><mfrac><mi mathvariant=\"normal\">k<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mfrac><mi>dt<\/mi><\/mrow><\/mstyle><\/math><br><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><mo stretchy=\"false\">\u21d2<\/mo><mfrac><msup><mi mathvariant=\"normal\">v<\/mi><mn>2<\/mn><\/msup><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mi mathvariant=\"normal\">k<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mfrac><mi mathvariant=\"normal\">t<\/mi><mo stretchy=\"false\">\u21d2<\/mo><mi mathvariant=\"normal\">v<\/mi><mo>=<\/mo><msqrt><mfrac><mrow><mn>2<\/mn><mi mathvariant=\"normal\">k<\/mi><\/mrow><mi mathvariant=\"normal\">m<\/mi><\/mfrac><mi mathvariant=\"normal\">t<\/mi><\/msqrt><\/mrow><\/mstyle><\/math><br><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><mi mathvariant=\"normal\">a<\/mi><mo>=<\/mo><mfrac><mi>dv<\/mi><mi>dt<\/mi><\/mfrac><mo>=<\/mo><msqrt><mfrac><mrow><mn>2<\/mn><mi mathvariant=\"normal\">k<\/mi><\/mrow><mi mathvariant=\"normal\">m<\/mi><\/mfrac><\/msqrt><mfenced separators=\"|\"><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><msup><mi mathvariant=\"normal\">t<\/mi><mrow><mo>\u2212<\/mo><mn>1<\/mn><mo>\/<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfenced><\/mrow><\/mstyle><\/math><br><math style=\"font-family:Arial;\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathsize=\"16px\"><mrow><mi mathvariant=\"normal\">F<\/mi><mo>=<\/mo><mi>ma<\/mi><mo>=<\/mo><mi mathvariant=\"normal\">m<\/mi><mfenced separators=\"|\"><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mfenced><msqrt><mfrac><mrow><mn>2<\/mn><mi mathvariant=\"normal\">k<\/mi><\/mrow><mi>mt<\/mi><\/mfrac><\/msqrt><mo stretchy=\"false\">\u21d2<\/mo><mi mathvariant=\"normal\">F<\/mi><mo>=<\/mo><msqrt><mfrac><mi>mk<\/mi><mrow><mn>2<\/mn><mi mathvariant=\"normal\">t<\/mi><\/mrow><\/mfrac><\/msqrt><\/mrow><\/mstyle><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A particle of mass m is driven by a machine that delivers a constant power k watts. 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