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A bicyclist is finishing his repair of a flat tire when a friend rides by at 3.5 m/s? |
A bicyclist is finishing his repair of a flat tire when a friend rides by at 3.5 m/s. Two seconds later, the bicyclist hops on his bike and accelerates at 2.8 m/s2 until he catches his friend. How much time does it take until he catches his friend? Since the friend has already traveled 3.5m x 2 seconds, the friend has a 7m "head start". That needs to be taken into account. The rest of it essentially involves setting up a formula that covers all the variables: You can begin to formulate the necessary formula by a small amount of "trial and error". Make a simple table, where column 1 is elapsed time, column 2 is where friend is, and column 3 is where you are: 0 friend passes you 1 3.5 0 2 7.0 0 3 10.5 2.8 4 14 8.4 (previous + 2x2.8) 5 17.5 16.8 See where this is going脡 Calculating how far the friend has gone after 2 seconds: Vfriend = 3.5 m/sec 鈭員 = 2 sec V = (鈭咲/鈭員) 3.5 m/sec = (鈭咲) / (2 sec) 鈭咲 = 7 m, how far the friend went after 2 seconds. He still has a constant velocity of 3.5 m/sec. aB (acceleration of bicyclist) = 2.8 m/sec虏 VoB = 0 鈭咲 = Vo鈭員 + (1/2)a鈭員虏 For the accelerating bycyclist: 鈭咲B = (0.5) aB 鈭員虏 鈭咲B = (0.5) (2.8 m/sec虏) 鈭員虏 鈭咲B = (1.4 m/sec虏) 鈭員虏 Now let's look at the friend's displacement: 鈭咲 = Vo鈭員 + (1/2)a鈭員虏 鈭咲F = V鈭員 鈭咲F = (3.5 m/sec) 鈭員 We know this from before: 鈭咲B = 鈭咲F + 7m (F = friend) Substitute 鈭咲F and 鈭咲B into the equation: (1.4 m/sec虏) 鈭員虏 - 7m = (3.5 m/sec) 鈭員 1.4 m/sec虏 (鈭員虏) - 3.5 m/sec (鈭員) - 7m = 0 Using the quadratic formula, I get: 鈭員 = 3.8117 sec OR -1.3117 sec Obviously, it can't be negitive, so we are left with the answer: 鈭員 = 3.8117 sec As to the previous answer of a trial and error table, there was a significant mistake: 鈭員 VFriend VBycyclist 0 friend passes you 1 3.5 0 2 7.0 0 3 10.5 2.8 4 14 8.4 (previous + 2x2.8) <-----NO! 5 17.5 16.8 This is wrong. Using the formula: Vf = Vo + a鈭員, starting from 2.8 m/sec, accelerating at 2.8 m/sec虏 for 1 sec: Vf = (2.8 m/sec) + (2.8 m/sec虏) (1 sec) Vf = 2.8 m/sec + 2.8 m/sec Vf = 5.6 m/sec at the end of the fourth second, not 8.4 m/sec!! And also, the velocity after 5 seconds would be 8.4 m/sec + 2.8 m/sec, ir 11.2 m/sec, NOT 16.8 m/sec!!! |
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