Motion in a straight: 6 problems

1. Calculate the average speed of the Earth in its orbit about the sun. (The radius of the orbit is 1.5 x 10^11 meters.) Give this in m/s and in miles/h. Now, what is the average velocity of the earth, averaged over one year's time?

2. Is it possible for speed to be constant while acceleration is not zero? Give an example.

3. A football halfback runs 15.0 m straight down the playing field in 2.50 s. He is hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Find his average velocity for each of the three intervals and for the entire motion.

4. Freight trains cannot accelerate very quickly. (A) Suppose a train accelerated for 8.00 minutes at a rate of 0.0500 m/s^2, starting with an initial velocity of 4.00 m/s. What is its final velocity? How far did it travel? (B) Now suppose the train slows down at a rate a = -0.550 m/s^2. How long will it take the train to come to a stop? What distance will it cover during the time it slows down?

8. (A) Make an accurate graph, on graph paper, of the position of an object undergoing constant acceleration according to the following equation:
x = (1/2)at^2 where a = 4.0 m/s^2 and the starting point is x = 0
Do this for time points from 0 to 6 seconds, spaced at 1-second intervals.
(B) Find the average velocity between t = 2 s and t = 6 s. By definition, this is just the total displacement divided by the time interval. Now, draw a line on the graph, between the position point at 2 s and that at 6 s. What is the slope of this line?
(C) Find the average velocity between t = 3 s and t = 5 s. Also draw a line between the position points at 3 s and 5 s. What do you notice?
(D) At what time is the instantaneous velocity equal to the average velocity you found in parts (B) and (C)?

9. (A) Make a graph of the velocity of an object as a function of time, according to the equation
v = at where a = 4.0 m/s^2 and the initial velocity is zero
Again, do this for time points from 0 to 6 seconds, spaced at 1-second intervals. This represents the same object you treated in the previous problem.
(B) Find the average velocity between t = 2 s and t = 6 s. We define this as (v_1 + v_2)/2 where v_1 and v_2 are the initial and final instantaneous velocities.
(C) Find the average velocity between t = 3 s and t = 5 s. Do you see why, from the graph, this is the same as you found in part (B)?