Hi everybody, I had 2 HW questions that I didn\'t get for my physics class, and

Question

Hi everybody,

I had 2 HW questions that I didn't get for my physics class, and Iwould really appreciated if you could explain them to me. They'repretty simple, I think, but the way they're worded makes itdifficult to picture.

1) Two trains, each having a speed of 30 km/hr, are headed at eachother on the same straight track. A bird that can fly 60 k /hrflies off the front of one train when they are 60 km apart andheads directly for the other train. On reaching the other train itflies directly back to the first train, and so forth. ( We have noidea why a bird would behave this way). What is the total distancethe bird travels?

2) If a particle's position is given by x= 4mp - (12m/s)t+(3m/s^2)(t^2), what is its velocity at t1 = 1 s?

For this problem, the correct answer is -6m/s (answers on the backof the book) but I don't know how to get that.


Thank you so much for your time!

Explanation / Answer

1.   This is kind of a trick question. Physics profslove giving it to first time students to test their ability tothink about what is being asked. . If the trains are 60 km apart and each is traveling 30 km/hr,it will take 1 hour for the trains to reach the same spot (theywill each travel 30 km). . During this one hour, the bird flies at a constant speed of 60km/hr. So during that time, the bird travels 60 km. . (forehead slap here). . 2.    position =  4   - 12 t    + 3 t2 . This involves calculus. The time derivative of the positionfunction gives the velocity function, so: .       velocity = derivative ofposition function =    - 12  + 6 t . So at   t = 1 sec,     velocity =    -12 + 6 * 1 =    -6 m/s . If you haven't yet done derivatives in calculus, you will.They're not bad... you just have to know the process to dothem. . This involves calculus. The time derivative of the positionfunction gives the velocity function, so: .       velocity = derivative ofposition function =    - 12  + 6 t . So at   t = 1 sec,     velocity =    -12 + 6 * 1 =    -6 m/s . If you haven't yet done derivatives in calculus, you will.They're not bad... you just have to know the process to dothem.

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