Motion in One Dimension Physics 2053 Lecture Notes dx dt x t Motion in One Dimension (2053)
Post on 14-Dec-2015
249 Views
Preview:
Transcript
Motion in 1 Dimension
v
In the study of kinematics, we consider a moving object as a particle.
A particle is a point-like mass having infinitesimal size and a finite mass.
Motion in One Dimension (2053)
0 2 4 6246
x
Displacement
Motion in 1 Dimension
The displacement of a particle is defined as its change in position.
(m)
x = x xo
= 6 m 2 m
= 4 m
Note: Motion to the right is positiveMotion in One Dimension (2053)
0 2 4 6246
x
Displacement
Motion in 1 Dimension
The displacement of a particle is defined as its change in position.
(m)
x = x xo
= 6 m 6 m
= 12 m
Note: Motion to the left is negativeMotion in One Dimension (2053)
0 2 4 6246
x
Displacement
Motion in 1 Dimension
The displacement of a particle is defined as its change in position.
(m)
x = x xo
= ( m) (6 m)
= 8 m
Note: Motion to the right is positiveMotion in One Dimension (2053)
Motion in 1 Dimension
Average velocity
The average velocity of a particle is defined as
x
t
x1
x2
t1 t2
x
tVelocity is represented
by the slope on a displacement-time graph
Motion in One Dimension (2053)
Motion in 1 Dimension
Average speed
The average speed of a particle is defined as
Motion in One Dimension (2053)
Motion in 1 Dimension
Average acceleration
The average acceleration of a particle is defined
as the change in velocity vx divided by the time
interval t during which that change occurred.
v
t
v1
v2
t1 t2
v
tAcceleration is
represented by the slope on a
velocity-time graph
Motion in One Dimension (2053)
Motion in 1 Dimension
Instantaneous acceleration
The instantaneous acceleration equals the derivative of the velocity with respect to time
v
t
v
t
Instantaneous acceleration is represented by
the slope of a velocity-time graph
Motion in One Dimension (2053)
Motion in 1 Dimension
t
x
t
v
t
a
Displacement, velocityand acceleration graphs
The slope of a velocity-timegraph represents acceleration
The slope of a displacement-timegraph represents velocity
Motion in One Dimension (2053)
Motion in 1 Dimension
t
x
t
v
t
a
t
Displacement, velocityand acceleration graphs
The area under an acceleration-timegraph represents change in velocity.
v
The area under a velocity-timegraph represents displacement.
x
Motion in One Dimension (2053)
Motion in 1 Dimension
Definitions of velocity and acceleration
Average velocity
Average acceleration
Motion in One Dimension (2053)
Motion in 1 Dimension
For constant acceleration
An object moving with an initial velocity vo undergoes
a constant acceleration a for a time t. Find the final velocity.vo
time = 0 time = t
Solution:
Eq 1
a ?
Motion in One Dimension (2053)
Motion in 1 DimensionFor constant acceleration
An object moving with a velocity vo is passing position xo when it undergoes a constant acceleration a for a time t. Find the object’s final position.
Solution:
time = 0 time = t
xo?
avo
Motion in One Dimension (2053)
Eq 2
Motion in 1 Dimension
Eq 1 Eq 2
Solve Eq 1 for a and sub into Eq 2:
Solve Eq 1 for t and sub into Eq 2:
Eq 3
Eq 4
Motion in One Dimension (2053)
(s)
x
48
1216202428
(m)
1 2 3 4 t5
1 2 3 4 5 t (s)
2
4
6
8
10
v
(m/s)Displacement
25 m
Motion in One Dimension (2053)
Review:
Average velocity
Average acceleration
Kinematics with Constant Acceleration
Motion in One Dimension (2053)
Definitions
Problem Solving Skills
1. Read the problem carefully
2. Sketch the problem
3. Visualize the physical situation
4. Strategize
5. Identify appropriate equations
6. Solve the equations
7. Check your answers
Motion in One Dimension (2053)
top related