A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m long stretch of black ice. Unfortunately, due to skidding, neither accelerating nor braking has any effect on the speed! The driver manages to maintain steady straight direction of motion and the only impact is provided by the ice friction force, which is numerically equal to 4v² Newtons, where the velocity v of the car is measured in m/sec. (a) Using Newton's Second Law F = ma, set up a mathematical model for the position x(t) and velocity v(t) of the car as functions of time t. Start by drawing a diagram and choosing a consistent system of units based on kg, m, sec (1 ton = 1000 kg, 1 m/sec = 3.6 km/h, 1 N = 1 kg · m/sec²). Introduce and label the variables, show the units and write down the differential equations and the intial conditions. (b) Use the model in part a to calculate v(t) and r(t). Fully show the process of solving the initial value problems. (c) Based on your work so far how long will it take to pass the iced over stretch of the road

A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m long stretch of black ice. Unfortunately, due to skidding, neither accelerating nor braking has any effect on the speed! The driver manages to maintain steady straight direction of motion and the only impact is provided by the ice friction force, which is numerically equal to 4v² Newtons, where the velocity v of the car is measured in m/sec. (a) Using Newton's Second Law F = ma, set up a mathematical model for the position x(t) and velocity v(t) of the car as functions of time t. Start by drawing a diagram and choosing a consistent system of units based on kg, m, sec (1 ton = 1000 kg, 1 m/sec = 3.6 km/h, 1 N = 1 kg · m/sec²). Introduce and label the variables, show the units and write down the differential equations and the intial conditions. (b) Use the model in part a to calculate v(t) and r(t). Fully show the process of solving the initial value problems. (c) Based on your work so far how long will it take to pass the iced over stretch of the road

Name: A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m
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Description: A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m long stretch of blackice. Unfortunately, due to skidding, neither accelerating nor braking has any effect on thespeed! The driver manages to maintain steady straight direction of m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

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Question

A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m long stretch of black
ice. Unfortunately, due to skidding, neither accelerating nor braking has any effect on the
speed! The driver manages to maintain steady straight direction of motion and the only
impact is provided by the ice friction force, which is numerically equal to 4v² Newtons, where
the velocity v of the car is measured in m/sec.
(a) Using Newton's Second Law F = ma, set up a mathematical model for the position
x(t) and velocity v(t) of the car as functions of time t. Start by drawing a diagram and
choosing a consistent system of units based on kg, m, sec (1 ton = 1000 kg, 1 m/sec =
3.6 km/h, 1 N = 1 kg · m/sec²). Introduce and label the variables, show the units and
write down the differential equations and the intial conditions.
(b) Use the model in part a to calculate v(t) and x(t). Fully show the process of solving the
initial value problems.
(c) Based on your work so far, how long will it take to pass the iced over stretch of the road
and how fast will the car be moving as it exits the ice?
Do not use a calculator! Leave your answers in an "algebraic" form, which may involve
exponential functions and logarithms, simplify as appropriate, and clearly specify the
units (e.g. sec, m/sec or km/h).

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