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Grade 10Mechanics

A particle of mass m is subjected to a net force src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAXCAIAAACeQxh6AAAAiUlEQVQ4jd3UwQ2AMAgFUOZioM7DNCzDMHqoiaUCLVpj4r/3hQ9JYVsU+A8khEiyAKoWFLYhLpDNQb01UUqZ2ZEQ2kXU4zb+RFy6d0IIZ5UkpN71beYgIQyKzENZx4V0MS7+cmLocrXhcDaki4VLjqHrxYYxoRuOCaUv5kB10U+h9lypct9/tX12VYTCBx7gnOAAAAAASUVORK5CYII=(t) given by src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAWCAIAAABL1vtsAAAAhklEQVQ4jdWUyw3AMAhDmYuBmIdpWIZh2kMrNRDyIcmlvvvJ2BJwbQv+ilBGZN1NoYxA4hFCkNULOZki5e93oYxxbGMrFaUQcg5lhC/4NMI4fPYRQhk7sWcQWUKAsGcItUtoIapFhoE8wp7RrbGFqNcYyiEWCA6RXqNCPFWuI8opUqcceHw3UnX2xB4l3fwAAAAASUVORK5CYII=(t) src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIYAAAAXCAIAAABBIaAgAAACCUlEQVRoge1Zy5XFIAhNXRZkPVbjajqxGGeRTCKggAZNzpnc1cyLInD5+Nnyh/WIftvhQiIftwcU+s84yPAx55xzCo4S81GyDNFfXECk4ApePkpeBztKjiSkqNXLOqKvjK7+uAwpuHP1poW7lT/BNbKAzG6PysZZEj1iIPFa4qlo5GXEY5SAeCj/AfpGf/7NBtDeSCR/2FMCVkzBKdxZYe40jdBsCDEBC19DW2D1j74U05ba7iYlLCmBevZNayo6jxJRXUYx3rkNUpT+MaRkkBEhVKdQQrtCy4MjjDRs0vrHkBKoZ/TjTYR8n5ElUp8rG3ttqljx8ADB0j1MXEgbnMGCdwyJPJUfReumUaLIzmFGakOkWRVKbgKuqGvrWdHxJEpGI0lYmCNM06XJfdivZN6OE17O5n71NySCEsgW2WrWpkkbELt1uK+eSknuFi13xMrBf00mUsGWL5UsX7li+nhGrLOH0BH0SW/tQL5Gdzu/KJedis3p2ozaUnK2p9hEGTG/4TKTkkIr3hnzf153AkQzWP0CyjxaUSJc3sC4Tg7lzFYYu8zuVRkLFxq7YTwIZ2sutv+BbcBNMswQqpr8IWwGusffIGDszG2WJBODy6gHsPaRYaDJ4dX3Gwor3ksLO5pG4Y0cyEfcZGX1KKA5yi56wriIsXGE8+DRy92nGKte/V8XX4aPkdfgFl19k/Sst+4IAAAAASUVORK5CYII= that is, F(t) equals Fo at t = 0 and decreases linearly to zero in time T. The particle passes the origin x = 0 with velocity src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAYCAIAAAD78wNdAAABBklEQVRIie2TsRGDMAxFf0mXbcidK49C5csg6eMR6Om9RY4BPAClS0qnMBgZDCjJQZGLKp2QeP5fNvzxgT/jVIZRAACh7TEMowAo4723WqxwvmEYNfx+s3TmPqwWGCMcY6qs2kyaFkfPMGI/bTZqE0DGthHUq2l9cXpnmHkQuo8EYtS+CJ6MdOcEYhRDBA8xu1cjJOPT8NBSZ1grm9/dANFapJOEST2cbZDJGK/jUkSskDzKyDkbhCuTeYNZi1cY0cCclpTheud6F77kc6vLomp6F0bLxzP2cALe+7ZrZS3DH2Uts/n1fkEFFMCtifU3GBEja9l2LT9nYqZ9hMnPci7juPgVxguuEEaVFAbUvgAAAABJRU5ErkJggg==. Show that at the instant t = T that F(t) vanishes, the speed v and distance x traveled are given by v(T) src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIMAAAAYCAIAAABWXtmxAAAB+klEQVRoge1Y0dnDIAh0LgdyHqdxGYfp/9CogCDE2PxpP++p0YgXDk+re208A+6/CWwc2Eo8BVuJp2ArYUeO3onwMQtDcE8KwqCthB0ptNyl4JwLqXWU3+KIomR98a1J7f4dJfryWz9BjZ+jB0lMgZ+ZKJSjR4K9lSkjtxJTQEtiQGj8TgqrlTi8D9aIbJ0dWcY2pXYtll0JMIOPOQUtrRhrhMBudVmJYwU2bsdXid6JiZTcgQepXcEJJVAtYo8wwUJKp0OiOMBtCGVivDe9ZO/EQ4BYdYDUrsCqBNk3GeqmCGfzwQaBpbpon+jiWtZ7cQjKWGonmKueLo26i7ATj0doQjD9i5SgkVMAT82Te3JS32gMD9uaMAkxntywJMbWzGu/xp1IbKRDYzWoJXK2VtsFDvqLlAOTVoWwLsR4lUnLZc2agJThsZvkB1Ekp+tKUGrXMKPEUfz0kM8TZiMIRMQX6GrJ0R+Pi5XotlecSPiEd872fVK7hvPulIKPsTAqG5tMGBAaMRqVTudaoOzWKFGNtWOI50YsiSOq7QYO9rNTJVtm428uSFoBtVGyhT7+3uqu/9h9iZ06ptyPi4Tnv/DTSnRbw20XEpO4RPj8ibjh4/dOgNw3CHGJ8BUhbrkBbO76cGcqmCR8+s86wu/cxX47thJPwVbiKfgDHxAWrBQEayAAAAAASUVORK5CYII= and x(T) src=data:image/png;base64,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, where src=data:image/png;base64,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 is the initial acceleration. Compare these results with Eqs. 2-26 and 2-28.

Profile image of Hrishant Goswami
11 Years agoGrade 10
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1 Answer

Profile image of Jitender Pal
11 Years ago
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Therefore the force experienced by the particle at t = T is zero .
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Therefore, the velocity matches the magnitude of velocity calculated above.
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Therefore, the position matches the magnitude of position calculated above