Try to follow the steps outlined in the Solving Problems section of this lecture when solving the problems below (or any kinematics problems in the future, for that matter!). See your instructor if you are having difficulties with this material — especially if you are still having troubles after the problems lab. This material will be fundamental to catching on to material later on in this course!
I. Warm-up Exercises
1. A car is sitting at a red light. The light turns green, and the car accelerates uniformly (in the positive-x direction) at 2.3 m/s2 for 4.7 s. (a) What is the x-component of the car’s velocity at the end of the given time period? (b) How far has the car moved during this time? (c) What was the car’s average x-component of velocity?
II. Some Standards
2. A car is moving with a speed of 27 m/s down a long, straight road. When it is 130 m from a traffic light, the light turns red. (a) With what constant acceleration must the car move in order to stop at the light? (b) How long does it take the car to stop?
3. A building is 45 m long. You run along the front of the building on your way to try to catch a bus. When you pass the first end of the building, you are running at 2.2 m/s . You are running at 4.1 m/s when you pass the other end of the building. Assume that you ran with a constant acceleration as you passed in front of the building. (a) What was the value of your acceleration? (b) How long did it take you to pass the front of the building? (c) What was your average velocity during this time?
4. Beverly butterfly has not been a butterfly for very long — as a matter of fact, she appeared as a debutante just 15 minutes ago. Needless to say, her mastery of her new and glorious wings is still lacking more than a little luster. A fairly steady wind has been blowing, carrying her with it, tumbling to and fro. Just one minute ago she was bustling along the smooth ground at 2.7 cm/s, while now she is seen to be pushed along at 5.1 cm/s (which is much too much for her taste!). Using the information given, determine Beverly’s acceleration (assumed constant).
III. So, you think you’re pretty good...?
5. Starting from rest, you move with a constant acceleration of 1.2 m/s2 in the positive-x direction for 12 s. At the end of the first 12 seconds, you switch to an acceleration of 0.95 m/s2 in the negative-x direction for another 12 s. (a) What was the maximum speed that you attained? (b) What was the total distance that you traveled during the whole trip? (c) What was your average speed for the trip? (d) What was your average x-component of velocity? (e) How do your answers to parts (c) and (d) compare? Will this always be the case? Why or why not?