University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 2.10CYU: Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by...
Related questions
Question
Trying to figure out how to prove the exercise on the bottom of the page.
![We usually write this in the form
1
(v²(1) - v² (0)] + (0). 31,and bus suis
2a
This equation, which of course holds only for constant acceleration since it comes from
our
handy equations for the special case,
and at t₁ we have
be very useful.
Before going to examples lets show first that our three equations for the special case
so much
of constant acceleration can be put in yet another form which does not depend
on when we started our clock or where we called a = 0. For example at t = 12 we hau
v(t₂) = at₂ + v(0)
v²(t)- v²(0) = 2a [z(t)-(0)].
Or
Subtracting the second from the first gives
and subtracting,
v(t₁) = at₁ +v(0).
v(t₂) = a (t₂-t₁) + v(t₁).
This really says the same thing as the original equation: The velocity at the end of a time
interval is the velocity at the beginning plus the acceleration times the time interval.
Doing the same thing for the second equation we have
v(t₂) - v(t₁)= a(t₂-t₁)
z(t₂) =
z(t₁) =
at² +v(0)t₂ + x(0)
2
1
at² +v(0)t₁ + 2(0)
2
1
x(t₂) - x(t₁) == a. (t²-1²)+v(0) (t₂-t₁)
2
Exercise: Go through the algebra to show that the above leads to noape brooss sel
1
-
z(t₂) — z(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁).
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0ee4640-6745-4736-a864-91941cf0214c%2Fa0c8f922-8b2c-4681-a230-3938e0a83601%2F6791b7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We usually write this in the form
1
(v²(1) - v² (0)] + (0). 31,and bus suis
2a
This equation, which of course holds only for constant acceleration since it comes from
our
handy equations for the special case,
and at t₁ we have
be very useful.
Before going to examples lets show first that our three equations for the special case
so much
of constant acceleration can be put in yet another form which does not depend
on when we started our clock or where we called a = 0. For example at t = 12 we hau
v(t₂) = at₂ + v(0)
v²(t)- v²(0) = 2a [z(t)-(0)].
Or
Subtracting the second from the first gives
and subtracting,
v(t₁) = at₁ +v(0).
v(t₂) = a (t₂-t₁) + v(t₁).
This really says the same thing as the original equation: The velocity at the end of a time
interval is the velocity at the beginning plus the acceleration times the time interval.
Doing the same thing for the second equation we have
v(t₂) - v(t₁)= a(t₂-t₁)
z(t₂) =
z(t₁) =
at² +v(0)t₂ + x(0)
2
1
at² +v(0)t₁ + 2(0)
2
1
x(t₂) - x(t₁) == a. (t²-1²)+v(0) (t₂-t₁)
2
Exercise: Go through the algebra to show that the above leads to noape brooss sel
1
-
z(t₂) — z(t₁) = a · (t₂ − t₁)² + v(t₁)(t2 − t₁).
2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
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.Recommended textbooks for you
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University