Basic kinematics - conceptual questions

[mizulyn]

Hello -- I'm an upcoming junior in high school, and I'm trying to study some physics by myself in preparation for the physics class I will be taking. However, I am confused on the following conceptual questions about kinematics:

1). Traffic lights are often timed so that if you travel at a certain constant speed, you can avoid all red lights. Discuss how the timing of the lights is determined, considering that the distance between them varies from one light to the next.

^ for this question, I said something about how timing is determined by the number of cars coming to the intersection vs. the cars passing the light, but I'm not sure that that's the answer that they're looking for.

2). The average velocity for a trip has a positive value. Is it possible for the instantaneous velocity at any point during the trip to have a negative value?

3). A ball is dropped from rest from the top of a building and strikes the ground with a speed of v. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is v0 = v, the same speed with which the first ball will eventually strike the ground. Ignoring air resistance, decide whether the balls cross paths at half the height of the building, above the halfway point, or below the halfway point.

4). The muzzle velocity of a gun is the velocity of the bullet when it leaves the barrel. The muzzle velocity of one rifle with a short barrel is greater than the muzzle velocity of another rifle that has a longer barrel. In which rifle is the acceleration of the bullet larger?"

Thank you very much for any help!

 

[spideyunlimit]

2) Yes, if you consider one direction as positive and fix the convention, then when you're traveling back, you'll be moving in an opposite direction so at any instant then you velocity will be negative.

 

[cryptoguy]

1) Perhaps they wanted you to relate the distance between lights and the average speed of a driver to the timing of the lights. For example if the average speed on a street is 5 m/s, and the distance between adjacent lights is 100 m, they try to make sure that the light is green about 20 secs after the previous light turns green.

3) think about the equation V_f^2 = V_i^2 +2ad. Set that equation equal to D and plug in some dummy values or apply reasoning to the two cases.

4) Once again V_f^2 = V_i^2 +2ad and solve for a this time. d will be the length of the barrel. You can also plug in dummy values for Vf and d, making sure they adhere to directions.