Traffic and Highway Engineering - With Mindtap
5th Edition
ISBN: 9781305360990
Author: Garber
Publisher: CENGAGE L
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Chapter 3, Problem 10P
To determine
The gap between the two vehicles after a given duration.
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Students have asked these similar questions
The gap between two consecutive automobiles (distance between the back of a vehicle and the
front of the following vehicle) is 65 . At a certain time, the front vehicle is traveling at 45 mi/h,
and the following vehicle at 35 mi/h. If both vehicles start accelerating at the same time,
determine the gap between the two vehicles after 15 sec., if the acceleration of the vehicles can
be assumed as follows, where u, in the equation is vehicle speed in ft /sec.
du
3.4-0.07u, (leading vehicle)
dt
du
3.3-0.065
dt
=
(following vehicle) ₂ 2
An impatient car driver stuck behind a slow-moving truck traveling at 25 mi/h decides to overtake the truck. The accelerating characteristic of the car is given by: dv/dt=3-0.05v where v is the speed (ft/sec) and t is the time (0sec).What is the acceleration in meter per second after 25 seconds?
Two automobiles A and B shown below are approaching each other in adjacent
highway lanes. At t = 0, A and B are 1km apart, their speeds are vA = 25 km/h and
vB = 20 km/h, and they are at points P and Q, respectively. Knowing that A passes
point Q 42 s after B was there and that B passes point P 40 s after A was there,
determine (a) the uniform accelerations of A and B, (b) when the vehicles pass
each other, (c) the speed of B at that time.
DA = 25 km/h
Ug = 20 km/h
B
1 km
Chapter 3 Solutions
Traffic and Highway Engineering - With Mindtap
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- Two automobiles A and B are approaching each other in adjacent highway lanes. At t=0, A and B are 1km apart, their speeds are 108km/h and 63km/h and they are at the points P and Q respectively. Knowing that A passes point Q 40s after B was there and B passes P 42s after A was there, determine the uniform acceleration of A and B, when the vehicles pass each other and the speed of B at that time.arrow_forwardThe gap between two consecutive automobiles (distance between the back of a vehicle and the front of the following vehicle) is 65 ft. At a certain time, the front vehicle is traveling at 45 mi/h, and the following vehicle at 35 mi/h. If both vehicles start accelerating at the same time, determine the gap between the two vehicles after 15 sec if the acceleration of the vehicles can be assumed to take the following forms: du/dt = 3.4 - 0.07u, (leading vehicle) du/dt = 3.3 - 0.065u, (following vehicle) where ut is the vehicle speed in ft /sec.arrow_forwardThe driver of the vehicle on a level road determined that she could increase her speed from rest to 51 kph in 36.80 seconds and from rest to 66 kph in 96.80 seconds. If it can be assumed that the acceleration of the vehicle takes the form du/dt = - βut where u is the vehicle speed in m/sec. Determine the maximum acceleration of the vehicle.arrow_forward
- A car is travelling along a straight horizontal road with a constant acceleration of 0.75 m/3. The car is travelling at 8 m/s when it passes a pillar box. 12 seconds later it passes a lamp post. Find a the distance between the pillar box and the lamp post, b the speed with which the car passes the lamp post.arrow_forwardA car is traveling around a circular track of 660-ft radius. If the magnitude of its total acceleration is 6.2 ft/sec² at the instant when its speed is 32 mi/hr, determine the rate at at which the car is changing its speed. Answer: at = ± ft/sec²arrow_forwardThe gap between 2 consecutive automobiles is 25 meters. At a certain time the front vehicle is traveling at 85 kph and the following vehicle at 60 kph. If both vehicles start accelerating at the same time, determine the gap between two vehicles after 21 seconds if the acceleration of the vehicles can be assumed to take the following forms: du / dt = 1.04 – 0.080ut (leading vehicle) du / dt = 1.03 - 0.075ut ( following vehicle)arrow_forward
- Two automobiles A and B are approaching each other in adjacent highway lanes. At t = 0, A and B are 3200 ft apart, their speeds are VA = 65 mi/h and vâ = 40 mi/h, and they are at points P and Q, respectively. Knowing that A passes point Q 40 s after B was there and that B passes point P 42 s after A was there, determine (a) the uniform accelerations of A and B, (b) when the vehicles pass each other, (c) the speed of B at that time. VA = 65 mi/h UB = 40 mi/h B P 3200 ftarrow_forwardA car is traveling around a circular track of 820-ft radius. If the magnitude of its total acceleration is 6.7 ft/sec? at the instant when its speed is 37 mi/hr, determine the rate a, at which the car is changing its speed.arrow_forwardIn traveling a distance of 2.0 km between points A and D, a car is driven at 106 km/h from A to B for t seconds and 47 km/h from C to D also for t seconds. If the brakes are applied for 3.7 seconds between B and C to give the car a uniform deceleration, calculate t and the distance s between A and B.arrow_forward
- Situation 1: Two automobiles A and B are approaching each other in adjacent highway lanes. At t = 0 seconds, A and B are 1 km apart, their speeds are VA = 110 kph and VB = 60 kph and they are at points P and Q respectively. Knowing that A passes point Q, 40 seconds after B was there and that B passes point P, 42 seconds after A was there. Question 6 Question 7 Question 8 Determine the time when they pass each other. Determine the speed of B when they pass each other. Determine the acceleration of A. 25.89 sec O 24,88 m/s O 0.139 m/s^2 O 20.89 sec O 25.12 m/s O -0.278 m/s^2 O 10.89 sec O 23.77 m/s O 0.34 m/s^2 15.89 sec O 22.54 m/s O 0.48 m/s^2arrow_forwardIn traveling a distance of 2.3 km between points A and D, a car is driven at 91 km/h from A to B for t seconds and 43 km/h from C to D also for t seconds. If the brakes are applied for 3.7 seconds between B and C to give the car a uniform deceleration, calculate t and the distances between A and B. Answers: t = 91 km/h S= 59.94 i 2300 B T C 2.3 km 43 km/h S kmarrow_forwardA car is stopped at an entrance ramp to a freeway; its driver is preparing to merge. At a certain moment while stopped, this driver observes a platoon of vehicles a distance x0 upstream and initiates the merge maneuver. The platoon approaches the entrance ramp at a constant speed v. The stopped car can accelerate from speed 0 to v at uniform acceleration rate a. Find the latest time at which the stopped car can safely start the merge maneuver; i.e., derive an expression for the “latest safe start time” in terms of the variables x0, v and a. Assume this latest time enables the platoon to maintain its constant speed and "just touch" the merging car's trajectory. Ignore the physical dimensions of the car.arrow_forward
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