federica bianco PRO
astro | data science | data for good
1D motion
Instructor: Dr. Bianco
TAs: Joey Betz; Lily Padlow
University of Delaware - Spring 2021
MATH REVIEW: quadratic equations
"quadratic" because the highest order is
it is the equation of a parabola
the "roots" (solutions) are 2 and are given by the quadratic formula
MATH REVIEW: quadratic equations
MATH REVIEW: quadratic equations
scribbled notes from class... sorry about my poor handwriting...
MATH REVIEW: quadratic equations
"quadratic" because the highest order is
it is the equation of a parabola
the "roots" (solutions) are 2 and are given by the quadratic formula
coefficients
MATH REVIEW: quadratic equations
"quadratic" because the highest order is
it is the equation of a parabola
the "roots" (solutions) are 2 and are given by the quadratic formula
second
order
first
order
zeroth
order
H&R CH2 1D motion - velocity - acceleration
to define quantities in the 3D space we need a frame of reference: we choose the
origin and direction of an axis
0
positive
negative
H&R CH2 1D motion - velocity - acceleration
0
positive
negative
is the position of my object of interest at time t
H&R CH2 1D motion - velocity - acceleration
sign: once I chose the positive direction of my axis the sign will fall accordingly.
: greek letter Delta (capital) indicates the difference between two quantities
0
positive
negative
H&R CH2 1D motion - velocity - acceleration
0
I can define it as a vector quantity: it has a magnitude and a direction (along my 1D axis for now)
positive
negative
H&R CH2 1D motion - velocity - acceleration
We often plot the 1-D motion axis vertically and the time horizontally
0
time
position
positive
negative
H&R CH2 1D motion - velocity - acceleration
this is a vector quantity
H&R CH2 1D motion - velocity - acceleration
0
t
x
AVERAGE VELOCITY
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
0
t
x
AVERAGE VELOCITY
H&R CH2 1D motion - velocity - acceleration
x
t
AVERAGE VELOCITY
INSTANTANEOUS VELOCITY
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
AVERAGE VELOCITY
t
0
t
v
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
AVERAGE VELOCITY
INSTANTANEOUS acceleration
example of motion graph:
position
velocity
acceleration
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
KEY POINTS:
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
Equations of motion in 1D
you do not need to memorize them necessarily but you should be extremely familiar with them and know how to use each one.
When you try and remember them on the fly, think about the dimensional analysis.
To equate to displacement, velocity needs to be multipled by time.
To equate displacement acceleration has to be multiplied by time-squared
In a few weeks, you should have solved enough problems that you will have them memorized without even trying!
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
KEY POINTS:
{
{
{
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
An exemplary case of constant acceleration
Mass [Me] | g [m/s] | |
---|---|---|
Venus | 0.05539 | 8.83 |
Mercury | 0.815 | 3.61 |
Earth | 1 | 9.8 |
Mars | 0.1075 | 3.38 |
Jupiter | 317.8 | 26.0 |
Saturn | 5.2 | 11.2 |
Uranus | 14.6 | 10.5 |
Neptune | 17.2 | 13.3 |
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
Two identical objects are dropped from the Tower of Pisa 1 second apart. What happens to the distance between the 2 balls during the
a) Remain the same.
b) Decrease.
c) Increase.
d) First increase, then decrease.
e) First decrease, then increase.
discuss for 8 min:
a) which is the right anwer?
b) which equation would you use to show it?
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
Two identical objects are dropped from the Tower of Pisa 1 second apart. What happens to the distance between the 2 balls during the
H&R CH2 1D motion - velocity - acceleration
H&R CH2 1D motion - velocity - acceleration
Two identical objects are dropped from the Tower of Pisa 1 second apart. What happens to the distance between the 2 balls during the
Two identical objects are dropped from the Tower of Pisa 1 second apart. What happens to the distance between the 2 balls during the
Because the distance is propotional to time
the distance increases linearly with time
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
STEP 1. Put together all the information you have
STEP 2. Put the info in a frame of reference
STEP 3. Identify the unknown quantity
STEP 4. Choose the equation with gives you the unknown you need
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
write it as a quadratic equation in t
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
write it as a quadratic equation in t
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
write it as a quadratic equation in t
5.4s
-3.0s
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side.
(a) How long does the package take
write it as a quadratic equation in t
5.4s
-3.0s
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By federica bianco
1D motion, coordinates, displacement, velocity, acceleration,