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Two cars traveling on the parallel lanes of a two-lane road. The cars' motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters.
 
 
- At which of the times do the two cars pass each other?
 
- At which of the lettered times, if any, does car #1 momentarily stop?
 
- At which of the lettered times, if any, does car #2 momentarily stop?
 
- At which of the lettered times are the cars moving with nearly identical velocity?
 

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Coleen Amado
Coleen AmadoLv10
8 Oct 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Two cars travel on the parallel lanes of a two-lane road. The cars are at the same location at t = 0s, and move in such a way as to produce the velocity (relative to the ground) vs. time graph shown in the figure. On the graph, one vertical block is equivalent to one velocity unit.

Rank car #1’s speed relative to the ground at the lettered times (A through E). Rank from largest to smallest. To rank items as equivalent, overlap them.

The figure shows three graphs, A, B, C, which collectively describe the motion of an object in one dimension. The horizontal axis of each graph is time (symbol t). The vertical axes of the graphs are different. For one graph the vertical axis is position (symbol x), for another, it is the velocity (symbol v), and for another, it is acceleration (symbol a). Where the axes across is the point of zero for both time and the quantity corresponding to the vertical axis. Part A: For which sequence of graphs is the vertical coordinate position, velocity, and acceleration, respectively? (e.g., If you think graph Y is position versus time, graph X is velocity versus time, and graph Z is acceleration versus time, then your answer is Y, X, Z.). Multiple choice: 1)C, A, B 2)A, C, B 3)C, B, A 4)B, C, A 5)B, A, C 6)A, B, C. Part (b) Which one of the following situations can be most accurately represented by the graph, consistent with your answer to part (a)? (1) A car driving in the negative x-direction suddenly shifts into reverse and, with tires spinning, slows to a momentary stop before beginning to move in the position x-direction. (2)A car driving in the position x-direction slams on its brakes and comes to rest. (3) A rock is dropped from the rest from the top of a tall building. Assume air drag can be neglected, in which case its speed increases by the same amount each second. Take upward to be the position x-direction. (4) A sprinter runs a 100-meter dash and she runs in the negative x-direction. Starting from rest, she has a constant acceleration for the first 50 meters, then a constant speed for the remaining 50. Multiple choices: 1)4, 2)3, 3)2, 4)1.

How fast can a racecar travel through a circular tum without skidding and hitting the wall? The answer could depend on several factors:

  • The weight of the car;
  • The friction between the tires and the road;
  • The radius of the circle;
  • The “steepness” of the turn.

In this project, we investigate this question for NASCAR racecars at the Bristol Motor Speedway in Tennessee. Before considering this track in particular, we use vector functions to develop the mathematics and physics necessary for answering questions such as this.

A car of mass m moves with constant angular speed to around a circular curve of radius R (Figure 3.20). The curve is banked at an angle . If the height of the car off the ground is h, then the position of the car at time t is given by the function

 

As the car moves around the curve, three forces act on it: gravity, the force exerted by the road (this force is perpendicular to the ground), and the friction force (Figure 3.21). Because describing the frictional force generated by the tires and the road is complex, we use a standard approximation for the frictional force. Assume that for some positive constant . The constant is called the coefficient of friction.

Let denote the maximum speed the car can attain through the curve without skidding. In other words, is the fastest speed at which the car can navigate the turn. When the car is navigate at this speed, the magnitude of the centripetal force is

 

The next three questions deal with developing a formula that relates the speed to the banking angle .

Now that we have a formula relating the maximum speed of the car and the banking angle, we are in a position to answer the questions like the one posed at the beginning of the project.

The Bristol Motor Speedway is a NASCAR short track in Bristol, Tennessee. The track has the approximate shape shown in Figure 3.22. Each end of the track is approximately semicircular, so when cars make turns they are traveling along an approximately circular curve. If a car takes the inside track and speeds along the bottom of turn 1, the car travels along a semicircle of radius approximately with a banking angle of . If the car decides to take the outside track and speeds along the top of turn 1, then the car travels along a semicircle with a banking angle of . (The track has variable angle banking.)

The coefficient of friction for a normal fire in Elly conditions is approximately . Therefore, we assume the coefficient for a NASCAR tire in dry conditions is approximately .

Before answering the following questions, note that it is easier to do computations in terms of feet and seconds, and then convert the answers to miles per hour as a final step.

11. Suppose the measured speed of a car going along the outside edge of the turn is . Estimate the coefficient of friction for the car’s tires.

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