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
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
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

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section6.3: Relative Velocity

Problem 27PP

See similar textbooks

Similar questions

On September 8, 2004, the Genesisspacecraft crashed in the Utah desert because its parachute did not open.The 210 kg capsule hit the ground at 311 km/h and penetrated the soilto a depth of 81.0 cm. What was its acceleration (in m/s2 and in g’s), assumed to be constant, during the crash?
As a baseball is being thrown, it goes from 0.0 to 40.0 m/s in 0.42 s. (a) What is the acceleration of the baseball?(b) What is the acceleration in g's?
A woodpecker’s brain is specially protected from large accelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker’s head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in meters per second squared and in multiples of g, where g = 9.80 m/s2. (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.50 mm (greater than the head and, hence, less acceleration of the brain). What is the brain’s acceleration, expressed in multiples of g?
A woodpecker’s brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker’s head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in m/s^2 and in multiples of g (g=9.80m/s^2). (b) Calculate the stopping time.
(a) Calculate the acceleration (in m/s2) of a skier heading down a 19.7° slope, assuming the coefficient of friction for waxed wood on wet snow. (You can neglect air resistance, and you will find the equation for the acceleration of any object down an incline where fk = ?kN, a = g(sin(?) − ?k cos(?)), to be useful.) m/s2 (b) Find the angle (in degrees) of the slope down which this skier could coast at a constant velocity. (You can neglect air resistance, and you will find the equation for the acceleration of any object down an incline where fk = ?kN, a = g(sin(?) − ?k cos(?)), to be useful.)
It was a dark and stormy night, when suddenly you saw a flashof lightning. Six and a half seconds later you heard the thunder.Given that the speed of sound in air is about 340 m>s, how faraway was the lightning bolt? (Ignore the travel time for the flashof light.)
The (c) answer is incorrect, the height the flea gets should be 0.051 m, not 4.95 x 10 ^ -6. Because its initial velocity after accelerating is 1 m / s, and the flea travels approximately 0.051 m before its velocity decreases to 0. Adding 0.051 m to 0.0005 m should get 0.051 m after rounding. Please check and edit the answer again.
A woodpecker’s brain is specially protected from largedecelerations by tendon-like attachments inside the skull.While pecking on a tree, the woodpecker’s head comes to astop from an initial velocity of 0.600 m/s in a distance of only2.00 mm. (a) Find the acceleration in m/s2and in multiplesof g (g= 9.80m/s2)⎠. (b) Calculate the stopping time. (c)The tendons cradling the brain stretch, making its stoppingdistance 4.50 mm (greater than the head and, hence, lessdeceleration of the brain). What is the brain’s deceleration,expressed in multiples of g ?
A woodpecker's brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker's head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in m/s2 and in multiples of g ⎝g = 9.80 m/s2⎞ (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.50 mm (greater than the head and, hence, less deceleration of the brain). What is the brain's deceleration, expressed in multiples of g ?
A truck started with 8 m/s and then speeded up to reach at a certain place in 1 hr with 0.005 m/s^2. (a) What is its final speed? (b) How far will it go?
A car traveling at 20 m/sm/s runs out of gas while traveling up a 9.0 degree slope. How far will it coast before starting to roll back down? Express your answer in meters.
A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find(i) how long will it take for the ball to strike the ground? (i) how long will it take for the ball to strike the ground? (iii) how high the ball will rise?