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Answer to Question #5244 in Calculus for Fabiana

Question #5244
In physics, momentum P is defined by P=mv (where m stands for mass and v stands for velocity). A block of frozen nitrogen initially has mass 2kg and travels at 8meters/sec. It is accelerating at 0.5meters/sec2 and losing mass by melting at 0.1kg/sec. What is the rate of change of the momentum after 4 seconds?
Expert's answer
The rate of change of the momentum
<img src="data:image/png;base64,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" alt="">
After 4 seconds:
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVcAAAA+CAIAAAAQ389pAAAH00lEQVR4nO2d0YGsIAxFrcuCrMdqbMZiZj9GMUACAaIyyz1fb/bNaAjkEhBw+gAAxmZ624CfZ1umaZqmZXvbEAAqgQq0s68zRAD8MFCBdrZlmtf9bSsAqAUq0My+zhAB8MtABeo4ZgOmaV7X5RwP7Ot8ThEc//wmCd4HAHoDKlDON6iPyN+WK9Tndf8OD9bFRf+8LN9UYVswhQj6BCpQjIv78xPt4iOFcP+L2QPQK1CBUvw+PXg+sK/zFeveB6QCoFugAoV4oR3FtveZ9v4QAdAvUIFC9nU+4/laL7Sv87J9YhFwH07t2BaMCkB3QAWKcY8HvuFPJv/l8QBWGIKOsVMB0kkG+NNp4BHk6nCgXsAXGxXw+726bwAzCpyNeumXI398oHosVEC5jv4XJsj+wzrARHWwCYJ1vZxrpExbsBuGKRKc+psqEqgKVCbxIf/Q4+V2FRB6E6Yt/kC/84IKGO9FSjiZLG3U/qTm7t6UqElQkavu6yxqS+sSTck/DahM8paVRD9/ouNsVoGECER/7l8GnlcBY5/IlzsWNXKt/LZ6sZl5iJZpJZSs/o4J/9ShMymVfjwWL6wKlKyHZ/JJkr0F2ppKPmkiGSHojPmi/WdVQHZUaFRLdZx/Xzbxv/k/l9YIb3hzUIWxkIyqWhVI++c0o8obKZPSHrrGA+fN/a9e7WfZmp5BxypQth5ePx5IfLucuxbtP54LZHM+i+q4biL45Z5Ox2jCIYyiWhWQBxNZ/zSRM2lZib4IS9DiZuKVpjXnkkYE2vXwcrPjrDKefTFZtF+m8fJXC/Bvru5VK6uDKtvRsM5VTt7lbVu/XLLSTvVuFVD4p4mESd/O3FtiEi84YT0Zj5JaDBZUQL0enq9sKQhTjb4847ph0f7TuYBSrVqqIxh2nEQqwGt5WY3QX5qFUTgRYDwi0Pjn87lnRBD9V9D9i8YkN7OUI6iAfj08F3BiENomXHojnUdzN39YBbT+aKuO/H+b14u7mEWv6sdKOn1qzI1fGRFs7OfzZ1yeFq9LbWu1vAoUrIdnKuX6U9AGbIefaiNdaOc181kVYB0ldOf11SFeibGjHd+DNv6k2QBt8kyO/wsqQMz2S8CX85SBoI1Em1kaEJ8R8Akoc1NBBphEyVYE1EaS2M8m4A/nApyjYi+1VsfH/3LUZgzrhUmbrWaDmevRGIrvXBwYkn8MjPauGw//Y5tpnRzfiIYOxy8Mhl8WaweVAvrW2kES2doZ+SqMNgw1Lxcr9fMvrOkEF0EDsai+AfYRkNC/uatvV2UbAwuc/WK9gBr8CpOffhYxwp5Cp5amU9f8jYJ89b0+VvHw7+16AVX4Aw2TChzjfAEyirrxLtHEGGIM/ARjqMCNOIGhR5IrlwYD0AVQgQaiFX3djAcAKAAqUE+0ihPjAfCTQAWqSa7ibH7eB8BjQAVqiZfvKLdQA9AZUIFa2FWcxypPcQ01AB0CFaiHPn8MVnkKa6gB6BGoAACjAxUAYHSgAgCMzgj7CH4BLPsH7zHAnsLuwRbAz7YM9iSlr/Uko7+b6OmDBlkLkodfq49zq7+9foea1l1kIwVva3TaX+WJ0fc0KT5Gs4VS05uYj/5uolYVaN0ukPDJEZ/sMZiWRwMFJxfljhXN35oEp7j/3UDLJP+0capiaLSmUCX36Ko/HP3dRI0q0Foi+ffbE68SCqcaslfWuCs+JJspQ7MKJPxTzXWMI/fCwHyhlPSXFCtUwDs0PRJgpkjyvlqx/Mx5dZk0NW2VGp0K0BPp3Emf6u3DCVMlh2wVrxL6VLgxbtzN5zKGSsJftDES0v45zShrUb5x6SMzyTdIhXp5hJRUMMMNryUFBwkxBtOi2ahJRgW+ucvpg929J4c9JTH6HXs5oxO1klYVXSpjkJf/FW8fTpvK++O6qtDKbXOqqw2qkv3cl8IQklUgG5VC6p31TyuxyVKh9vJ3ZEUiQL+zeUdUEJ1xPyFpiN2clmpE4Dd2b2m83I45A02ncxJWZX+n7yXiw/BzhS8wlbvA/uSrhDwD+KAr7VR1KhD+gi0Oa5DCP63oVYDY6Z0wQ3qNdFLx4WszUAbpEAsrVCrglcV/LSIfCNJzEDFsavK3hFV6cnpqs31YMpXxRzR5zmR+Zm4Mu6qsvChzgXAUqEm3lHGs8Y+7ZmGLkk1OFiqS0lClfKuEIR69gV/I5PDbBI0KkHvHrYAzTDTWshSCVa72dffJNGs/3oLWoS6N7MDMJUrnBQqJos9CBZh+UjOVUFWgx0YEyUJ5VmzVb466bpFKpW+ZXS9RAbbrE1IcV5ywkZmVgrXKtVLtwxiFChRtH2aLKDsw4xG+1di50UtlNVPfqqGolMJeCX4cRXXB/JwKJPLyUASmsC3Q+eT4slwWEV6SDg7I1c1iSaMCZ/fK+1sa6cSZl62UcVaR2Fdm61lfuuRsUW0fZsuYcGDCJ/TBhPInFXiZc/ayyqbHz277KpDM5zVI/mkgHkaQSwtT9vJ4IEj0uXqTUn9qSHgzbV0V8L/eTUQaqTIZsFTUz6dgqoD+osgtrz5ttnbXQNyWzhvwv/YRkNB/o71W3rPANz03JZBCO0R9hX+2p9B1lF07nUExQfagG4E1r2ZwWf7d+QJ0HA8AUPDvVAAAUAhUAIDRgQoAMDpQAQBGByoAwOhABQAYHagAAKMDFQBgdP4AHUMIUnqCXOAAAAAASUVORK5CYII=" alt="">
And we have
<img src="data:image/png;base64,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" alt="">
answer:
<img src="data:image/png;base64,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" alt="">

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