Question

A car increases its speed from 39 km/hr to 75 km/hr in 10 seconds. Its acceleration is a) 3 m/s2 b) 0.8 m/s 2 c) 1 m/s2 d) 8 m/s2

Answer 1

Answer:

Solutions to the Problems

Problems of Chapter 2

2.1 Floating-Car Data

GPS data provide space-time data points and (anonymized) IDs of the equipped

vehicles. We can obtain their trajectories by connecting the data points in a space-

time diagram (via a map-matching process). From the trajectories, we can infer the

speed by taking the gradients. Low speeds on a highway or freeway, e.g., 30 km/h,

usually indicate a traffic jam. Since the data provide spatiotemporal positions of the

vehicles, we can deduce the location of congested zones, including their upstream

and downstream boundaries, at least, if the penetration rate of equipped vehicles

with activated communication is sufficiently high.1 However, GPS measurements

are only accurate to the order of 10 m and careful map-matching/error checking is

necessary to exclude, for example, stopped vehicles on the shoulder or at a rest area,

or vehicles on a parallel road. Moreover, due to this resolution limit, GPS data do

not reveal lane information, nor information on lane changes. Since the percentage

of equipped vehicles with connected devices is low, variable, and unknown, we can

not deduce extensive quantities (traffic density and flow) from this type of data.

To wrap it up: (1) yes; (2) no; (3) no; (4) no; (5) yes; (6) yes.

2.2 Analysis of Empirical Trajectory Data

1. Flow, density, and speed: Using the spatiotemporal region [10 s, 30 s] ×

[20 m, 80 m] suggested for a representative free-flow situation, we obtain by tra-

jectory counting:

1 On major roads with high traffic flow, 0.5 % of the vehicles are typically enough; on smaller roads,

we need a significantly higher percentage.

M. Treiber and A. Kesting, Traffic Flow Dynamics, 423

DOI: 10.1007/978-3-642-32460-4, © Springer-Verlag Berlin Heidelberg 2013

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