**Practice Problems: Motion Studies**Click here to see the solution.

1. (easy) A woman walks in a straight line for 40 minutes at an average speed of 1.25 m/s. How far does she travel in this time?

2. (easy) Interstate 70 is a highway that runs through the heartland of the United States. If traveler A drove 100 miles along Interstate 70 at 65 mph and traveler B drove the same distance at 55 mph, how much earlier would traveler A arrive?

3. (easy) In a well-formed paragraph, using the concepts described in the presentation, explain why the following statement must be incorrect: "The displacement of an object during an experiment was zero, but the average velocity was not zero." Additionally, how could you change the statement (replace one word with a different word) that would allow it to be true?

4. (moderate) A car is traveling along a road. It moves according to the following equation: x = 2.0t^{2} + 0.25t^{3} (x is in meters and t is in seconds) a) What is the average velocity of the car between 0.0 and 2.0 seconds? b) What is the average velocity between 2.0 and 4.0 seconds?

5. (moderate) Based upon the following data determine if the average acceleration of the object between 2.0 and 4.0 seconds has a bigger or smaller magnitude than the average acceleration between 4.0 and 6.0 seconds:

velocity at 2.0 seconds is 0.8 m/s

velocity at 4.0 seconds is 1.2 m/s

velocity at 6.0 seconds is 0.6 m/s

6. (moderate) A particle undergoes motion according to the equation: x = 5t^{4} - 2t^{2} - 8 where x is in meters and t is in seconds. Find the average speed of the particle over the first 7 seconds and the instantaneous speed of the particle at 5.0 seconds. Also, find the instantaneous acceleration at 0.5 seconds.

7. (moderate) A particle changes speed (in m/s) as it moves along the x axis according to the following equation: v = t^{2} - 4t + 9

Find the average acceleration of the particle between t = 5 seconds and t = 10 seconds and the instantaneous acceleration at each of those times.

8. (hard) A student jogs from home to the store. She runs at 1 m/s for 1/3 of the time and 1.5 m/s for the remaining time. On her way back home she runs at 1 m/s for half the distance and at 1.5 m/s for the rest of the trip. Find her average speed for the round trip.

9. (moderate) An object is bobbing up and down on the end of a long elastic cord according to the equation y = 5cos(3t), such that when t is in seconds, y is in in meters. Find the speed and the magnitude of the acceleration at t = 3.2 s.

**Please supplement these problems with those found in your companion text.**