The rectilinear motion of a particle is governed by the equation a = 6t – 4 where a is in m/s^2 and t is in seconds. When t=0, the acceleration of the particle is 4 m/s^2 to the left. During the interval from t=2 to t=45, the displacement of the particle is 20 m to the right. Determine: a. The initial velocity of the particle b. The velocity of the particle at the end of the displacement period c The position of the particle when t=3s

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)...
icon
Related questions
icon
Concept explainers
Topic Video
Question

NO.3 ONLY 

! COMPLETE SOLUTION !

*draw FBD

*use data given below properly

1. A particle moves along a straight line so that after t seconds its displacement s in meters from a
fixed reference point O on the line is given by: s =- 4 + 302 – 48t + 12. The particle is
4m to the left of the origin at t= 25. Determine
a. The acceleration of the particle when t=35
b. The displacement during the interval from t=2s to t=5s
c. The total distance traveled during the interval from t=2s to t=5s
d. The average velocity during the interval from t=2s to t=55
2. The resistance to motion of a particle in air is approximately proportional to the square of its
velocity v for speeds not exceeding 150 m/s. Thus, the deceleration is given by the expression
a =- ku', where k is taken to be a constant whose numerical value depends on the prevailing
air conditions and the shape, roughness, and mass. If a particle which moves in a horizontal
straight line is fired with an initial velocity of 50 m/s for a condition where k-1/100m*, in what
distance and elapsed time after firing will the velocity be reduced to 8m/s?
3. The rectilinear motion of a particle is governed by the equation a = 6t – 4 where a is in m/s^2
and t is in seconds. When t-0, the acceleration of the particle is 4 m/s^2 to the left. During the
interval from t=2 to t=45, the displacement of the particle is 20 m to the right. Determine:
a. The initial velocity of the particle
b. The velocity of the particle at the end of the displacement period
c. The position of the particle when t=3s
4. An average car can decelerate at the maximum rate of 8m/s^2 on the highway. Find the total
emergency stopping distance measured from the point where the driver first sights the danger
for a car traveling at a speed of 108km/hr. The reaction time for a good driver is about % of a
second from the instant he sights the danger until he actually applies the brakes.
5. A stone is dropped from a balloon which rises vertically at a constant rate for 4 seconds from the
ground. The stone reaches the ground in 10 seconds. Find the velocity and height of the balloon
when the stone is dropped.
Transcribed Image Text:1. A particle moves along a straight line so that after t seconds its displacement s in meters from a fixed reference point O on the line is given by: s =- 4 + 302 – 48t + 12. The particle is 4m to the left of the origin at t= 25. Determine a. The acceleration of the particle when t=35 b. The displacement during the interval from t=2s to t=5s c. The total distance traveled during the interval from t=2s to t=5s d. The average velocity during the interval from t=2s to t=55 2. The resistance to motion of a particle in air is approximately proportional to the square of its velocity v for speeds not exceeding 150 m/s. Thus, the deceleration is given by the expression a =- ku', where k is taken to be a constant whose numerical value depends on the prevailing air conditions and the shape, roughness, and mass. If a particle which moves in a horizontal straight line is fired with an initial velocity of 50 m/s for a condition where k-1/100m*, in what distance and elapsed time after firing will the velocity be reduced to 8m/s? 3. The rectilinear motion of a particle is governed by the equation a = 6t – 4 where a is in m/s^2 and t is in seconds. When t-0, the acceleration of the particle is 4 m/s^2 to the left. During the interval from t=2 to t=45, the displacement of the particle is 20 m to the right. Determine: a. The initial velocity of the particle b. The velocity of the particle at the end of the displacement period c. The position of the particle when t=3s 4. An average car can decelerate at the maximum rate of 8m/s^2 on the highway. Find the total emergency stopping distance measured from the point where the driver first sights the danger for a car traveling at a speed of 108km/hr. The reaction time for a good driver is about % of a second from the instant he sights the danger until he actually applies the brakes. 5. A stone is dropped from a balloon which rises vertically at a constant rate for 4 seconds from the ground. The stone reaches the ground in 10 seconds. Find the velocity and height of the balloon when the stone is dropped.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Displacement, velocity and acceleration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON