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Answer to Question #5365 in Mechanics | Relativity for Damany Wallace

Question #5365
Physics help (Kinetic Energy)

A bead with mass (1.8x10^-2)kg is moving along a wire in the positive direction of an x axis. Beginning at time=0, when the bead passes through x=0 with speed 12m/s, a constant force acts on the bead, the picture indicates the bead's position at these four times: t0=0 sec., t1=1.0 sec., t2=2.0 sec., t3=3.0 sec., The bead momentarily stops at t=3.0 sec. What's the kinetic energy of the bead as t=10 sec?

Do I use the K=(.5)mv^2 formula
or
the vf^2=vi^2+2ad formula, THEN the K-formula?
Expert's answer
1. You can find the first acceleration imparted to the bead constant force.
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUgAAAAeCAIAAADB1hA6AAAD/UlEQVR4nO1cyYGDMAykLgpyPa7GzVBM9sFlnT6wSBY0PwLB8kgjyXZ2p4/D4Xgcpm8b4HA4xsOF7XA8EC5sh+OBcGE7HA+EC9vh+I9Y4jztCIncdmE7HP8OS5wPNafASXuIsFOYpjkumhVcUnGMQIH8A+6FpyIFA2Hz6UJ4sCb+HPVgyM8bNIbwm7xQaBOfgSXO48lc4tz6TlbX14TdWARc2yNByV/ldHyUwne0naeb1YYnanvLXYOZbHdOCvwXLghblrVo3uulPYwAjvx84XU8w3jI1Au4jqUgh38K9EYK/yENLHGeQhjOI198u57vF7YYHlqL8m5lj2veqniUhG3pBTJF0YjDEnyzenX3NawZdHgr3tEAy09Lwl57qNNufM3TD1d4XKtiqeyizfbICJjjksLBUJmZDH3ks7bwo9h5gVqmlezP58Pb2S4akfnh2BsjzsbNU9vg+9X2ELpkZ8A0YRmyu6AFZ1ofTthbKjh9tNGUpwiZeT3vmOw4VNpsDRDCq0vATKsy8jXyeVsIrLzA1We9ZCsPVX1xRYn5gTh3tzCJu+DXrJly+U8h7sskMSfTbTMQLzB49hwhlwmlFSdpPU8Scs0oVAP1NrGXoOAv1WZTkDCkE22pk53kwxwvD2blhV5hn+MysV0grYL5QbOD6pOyI9q05C7rlkfwoyXOLZEsC5vUF9DeiLFV6hJNV1C6zRXo9jq/tqQ9aaU1neSTV0iPWXnhkrB3w/CzenKuYH4UYFE9BwadMLKHu6zc9mhjDkEWNh4K9vFSZBRZNd0+U20+a9n48Suiqyne+sjn3nLz8QQ1rb7t76rYN+payfqikDHTAvHCinEP2Q5XicJG/ODludaHtO6UwG93t0m6zSd1FtUKv5OZZouWOslnXyMGjIkX6Jsb2oueNXYF8+NmR20u/UwAmccHgZ6LNoMbI1YUdm4R197z/vp+weZtBk2UQU6HbHBdcHPBbieftKxixTb0Ah6zrOtru+Jl5q3A2oimi7zOB4GwHY6zVdukysKWVjhscOST5da3tufYss1w3PFWwHnPMe4jHCRIzLCB30c+0pRc8Uy9ALrnkkC52bd1VGXmrVCTkKRGHEeAXvh7DjH0VlzNfmwayTZl7/1lBBicTSilhmjQ2NmpBk3e1Dw2jDvJx8eewhyNvQDN0Ns3akb7L8+KzFsAHpsfH+uNOGuc0p03rw4yvOS34rRi33W4XUI3Kb0Lii96wUFhFYsv+esuctb/K6F9ya/t24Cu6t+C3Rb+iL/HLi0B7KyvR2bDD+l6wDqwev31C15wQBj65EX/QeU85/DwdvwCLPunFwnb4XgPXNgOxwPhwnY4HggXtsPxQLiwHY4H4g+xf/E83OQpIAAAAABJRU5ErkJggg==" alt="">
2. After 3 second the bead will move in another way with speed
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAAYCAIAAADPisJBAAAA/0lEQVRYhe2W0Q3DIAxEPRcDeR6m8TIMQz9Cgn1GaagCoVLuz4Dg6XI4UP4f0dMAHVqONcVAu1jM1FqswpVQGHFXYk0xEIWY9lqYTL0QK6KWOFRnNevmel2O9WDpAKiRejypYRa1XphYjvEJQhf9EGRAGHwU7vW1fI0TtTfsZU0x2OXF3RnqZUVbhVVVO9+YBPu8wm0zrGCrIa3B9Xv6I3/IgO8DeJJh1XMpBvD0KF1SbhL2UzSlzepulA2Hu4E3aUtZ2dnb7DPQ+BFj6xrFmk+fA1f/W97XWe1B6SKriagJ70RdfQ8o2KdQe94utRk98P1zXuqd9VUv6xi9rGP0AeDMkxUFu0yvAAAAAElFTkSuQmCC" alt="">
3. After 10 second the speed of the bead is
<img src="data:image/png;base64,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" alt="">
4. Kinetic energy
<img style="width: 139px; height: 59px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAABMCAIAAACpshFoAAADW0lEQVR4nO2b0aGrIBAFrcuCrMdqbMZieB9RA7tHIOq7UTLzp4lIYFwWJF0AUHTfrgDcFMwADWaABjNAgxmgwQzQYAZoMAM0mAEazAANZoAGM0CDGaDBDNBgBmgwAzSYEUKYx75bGaZv1+YmYMY89psO04AbK5iRMA2YsYAZMYjxBjPeTEPXj/O3a3EXMGOBcGHAjBDQQvEwM6YhnluuR8sYYA6TK7Zz9jiYUWQaGFFCCI8yY51eTkPX9eO0HL3WIoZxnXvGE88lFLxPTcNWwhYiVp82MCOE8CgzVl5daYJAepiODC+V0jhC95d4nhnz2McdrQ5TMdypJXJAlseZYUywAcHFB3+KTKKKx5khTIgigBDDhAy8qORpZhgTTLeLsSS5Yh57vKjkYWbUjiVRKrGZQd75EQ8zIz+W2PWOEEL0ip2s8yMeZgb8GZjRCvPYXxoVz5khNkOxP0oTt0tMpo2yTemWbvfKWkvJlaAuPB0zXuXHRS9VQYuEeOvYdiKTEttV/uLC7s49c9/Kfn6NGTYJZA7gsAuveTHUHMy/Kcw2s5rBF+6ScNYMsTiNFhXkd5y6LlveG9Y/gFU7WrNlnDQj+Qnscqim0HH+Yxc0sr1aGKmqKnHSjK3witgFK6WO8xHCn5qGruv7d4rqIkw/znEK629XqMV1c5NqMVRWnXLX8eiimhef6BozkkfRpJJuC5NKYUvj0Skzour6FOl6St1yMf/rZ5RTgBozMpeo7+oUNleNU7/fvKy678N+J2pyQ/+dYvNGXa/M0DltrsAzZqQelqxOL8tyV8EuqHndA+S/VfTJrX8UzCgWeMKMz28GtZHVBn/btO69cXKBf0hlApvvq+NmiAW0v0g2Hk2mP0ySmLTuTgiJN7x3ouP3ElRZouOgGWpJPzpH4JDkHtTdtww7DWpGtp1J6V4BFeG94XetSdsRyWJqxv02zTDDqvnjwc9TlRC2a4YPzKgRQqjOgts0w0FuHMLO3zv3+A0zqtdaYOMnzGB99gA/YAavgQ/RvBlsMTtI22YQLo7TshmEizO0a4bde3j1/zFap1Uz3J5Ut6sf8rRphv7bDyPLJ7RpBpwHM0CDGaDBDNBgBmgwAzSYARrMAA1mgAYzQIMZoMEM0GAGaDADNJgBmn/Nb5FOqV+SAwAAAABJRU5ErkJggg==" alt="">

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