A wagon filled with sand has a hole so that sand leaks through the bottom at a constant rate ฮป. An external force ๐น โƒ— acts on the wagon in the direction of motion. Assuming instantaneous velocity of the wagon to be ๐‘‰ โƒ— and initial mass of system to be m0, the force equation governing the motion of the wagon is ๐น โƒ— = ๐‘š_0 (๐‘‘๐‘‰ โƒ—" " )/๐‘‘๐‘ฅ + ฮป๐‘‰ โƒ— ๐น โƒ— = ๐‘š_0 (๐‘‘๐‘‰ โƒ—" " )/๐‘‘๐‘ฅ - ฮป ๐‘‰ โƒ— ๐น โƒ— = (๐‘š_0โˆ’"ฮป " ๐‘ก)(๐‘‘๐‘‰ โƒ—" " )/๐‘‘๐‘ฅ (๐‘š_0โˆ’"ฮป " ๐‘ก)(๐‘‘๐‘‰ โƒ—" " )/๐‘‘๐‘ฅ + ฮป ๐‘‰ โƒ—

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