Motion
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- Pages: 30
Describing Motion:
•Graphical Analysis of Linear Motion •Average Velocity •Instantaneous Velocity •Acceleration •Motion at Constant Acceleration •Solving Problems •Falling Objects
Graphing Velocity I The graph of position versus time for a car is given below. What can you say about the velocity of the car over time?
1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure
x
t
Graphing Velocity I The graph of position versus time for a car is given below. What can you say about the velocity of the car over time?
1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure
x
The car moves at a constant velocity because the x vs. t plot shows a straight line. The slope of a straight line is constant. Remember that the slope of x versus t is the velocity! t
Graphing Velocity II 1) it speeds up all the time The graph of position vs.
2) it slows down all the time
time for a car is given below.
3) it moves at constant velocity
What can you say about the
4) sometimes it speeds up and
velocity of the car over time?
sometimes it slows down 5) not really sure
x
t
Graphing Velocity II 1) it speeds up all the time The graph of position vs.
2) it slows down all the time
time for a car is given below.
3) it moves at constant velocity
What can you say about the
4) sometimes it speeds up and
velocity of the car over time?
sometimes it slows down 5) not really sure
The car slows down all the time because the slope of the x vs. t graph is diminishing as time goes on. Remember that the slope of x vs. t is the velocity! At large t, the value of the position x does not change, indicating that the car must be at rest.
x
t
v
v
1
3
t v
2
t
You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this motion?
(Assume
your y-axis is pointing up.)
Rubber Balls I t
4
v t
Rubber Balls I v
v
1
3
t v
2
t
You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this motion?
(Assume
your y-axis is pointing up.)
t
v
4
t
The ball is dropped from rest, so its initial velocity is zero. zero Since the yaxis is pointing upwards and the ball is falling downwards, its velocity is negative and becomes more and more negative as it accelerates downward.
v
v
1 v
3
t
2 You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the above plots represents the v vs. t graph for this motion? (Assume your y-axis is pointing up.)
t
Rubber Balls II t
v
4
t
Rubber v Balls II
v
1 v
3
t
2
t
t
v
4
t
You toss a ball straight up in the air and catch it again. Right
The ball has an initial velocity that is
after it leaves your hand and
positive but diminishing as it slows. It
before you catch it, which of the above plots represents the v vs.
stops at the top (v = 0), and then its
t graph for this motion?
velocity becomes negative and
(Assume your y-axis is pointing
becomes more and more negative as
up.)
it accelerates downward.
This is a graph of x vs. t for an object moving with constant velocity.
The velocity is the gradient of the graph. Calculate the velocity. Velocity = 11/1.0 = 11 ms-1
This is a graph of velocity vs. time for an object with varying velocity;
The acceleration = gradient of the graph distance travelled = Area under graph
Describe motion in words. 1. Acceleration
2. Constant speed
3. Deceleration
4. Constant speed
Calculate: 1. Acceleration 2. Distance
For each section
Calculating Instantaneous velocity
Velocity = gradient of the tangent
Average Velocity Speed: how far an object travels in a given time interval
Velocity includes directional information:
Veloc ity ms-1 10
10
20
25
32
Time (s)
-10
CALCULATE AVERAGE SPEED AND AVERAGE VELOCITY
ACCELERATION Acceleration is the rate of change of velocity.
ACCELERATION Acceleration is a vector In one-dimensional motion we only need the sign. This is negative acceleration:
vf
vi
t
Gradient = vf – vi / t = a vf = vi + at
vf
vi
t
area = 0.5 (vf – vi) x t + vi x t = d vf - vi = at d= 0.5 (at) x t + vi x t = vit + 0.5at2
MOTION AT CONSTANT ACCELERATION Combining these equations allows us to develop 5 equations each with 4 variables vf = vi +at d= vit + 0.5at2 vf2 = vi2 + 2ad d = (vf +vi)t / 2 d = vf t – 0.5at2
Each equation has one missing variable out of the 5 used (d, vi, vf, a, t)
SOLVING PROBLEMS 1. Read the whole problem and make sure you understand it. Then read it again. 2. Write down the known (given) quantities, and then the unknown ones that you need to find 3. What physics applies here? Plan an approach to a solution.
SOLVING PROBLEMS 4. Which equations relate the known and unknown quantities? Are they valid in this situation? Solve algebraically for the unknown quantities, and check that your result is sensible (correct dimensions). 5. Calculate the solution and round it to the appropriate number of significant figures.
SOLVING PROBLEMS 6. Look at the result – is it reasonable? Does it agree with a rough estimate?
7. Check the units again.
FALLING OBJECTS Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity. This is one of the most common examples of motion with constant acceleration.
FALLING OBJECTS
In the absence of air resistance, all objects fall with the same acceleration, although this may be hard to tell by testing in an environment where there is air resistance.
FALLING OBJECTS
The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s2.
Summary • Kinematics is the description of how objects move with respect to a defined reference frame. • Displacement is the change in position of an object. • Average speed is the distance traveled divided by the time it took; average velocity is the displacement divided by the time. • Instantaneous velocity is the limit as the time becomes infinitesimally short.
Summary • Average acceleration is the change in velocity divided by the time. • Instantaneous acceleration is the limit as the time interval becomes infinitesimally small. • The equations of motion for constant acceleration are given, there are five, each one of which requires a different set of quantities. • Objects falling (or having been projected) near the surface of the Earth experience a gravitational acceleration of 9.80 m/s2.
•Graphical Analysis of Linear Motion •Average Velocity •Instantaneous Velocity •Acceleration •Motion at Constant Acceleration •Solving Problems •Falling Objects
Graphing Velocity I The graph of position versus time for a car is given below. What can you say about the velocity of the car over time?
1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure
x
t
Graphing Velocity I The graph of position versus time for a car is given below. What can you say about the velocity of the car over time?
1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure
x
The car moves at a constant velocity because the x vs. t plot shows a straight line. The slope of a straight line is constant. Remember that the slope of x versus t is the velocity! t
Graphing Velocity II 1) it speeds up all the time The graph of position vs.
2) it slows down all the time
time for a car is given below.
3) it moves at constant velocity
What can you say about the
4) sometimes it speeds up and
velocity of the car over time?
sometimes it slows down 5) not really sure
x
t
Graphing Velocity II 1) it speeds up all the time The graph of position vs.
2) it slows down all the time
time for a car is given below.
3) it moves at constant velocity
What can you say about the
4) sometimes it speeds up and
velocity of the car over time?
sometimes it slows down 5) not really sure
The car slows down all the time because the slope of the x vs. t graph is diminishing as time goes on. Remember that the slope of x vs. t is the velocity! At large t, the value of the position x does not change, indicating that the car must be at rest.
x
t
v
v
1
3
t v
2
t
You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this motion?
(Assume
your y-axis is pointing up.)
Rubber Balls I t
4
v t
Rubber Balls I v
v
1
3
t v
2
t
You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this motion?
(Assume
your y-axis is pointing up.)
t
v
4
t
The ball is dropped from rest, so its initial velocity is zero. zero Since the yaxis is pointing upwards and the ball is falling downwards, its velocity is negative and becomes more and more negative as it accelerates downward.
v
v
1 v
3
t
2 You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the above plots represents the v vs. t graph for this motion? (Assume your y-axis is pointing up.)
t
Rubber Balls II t
v
4
t
Rubber v Balls II
v
1 v
3
t
2
t
t
v
4
t
You toss a ball straight up in the air and catch it again. Right
The ball has an initial velocity that is
after it leaves your hand and
positive but diminishing as it slows. It
before you catch it, which of the above plots represents the v vs.
stops at the top (v = 0), and then its
t graph for this motion?
velocity becomes negative and
(Assume your y-axis is pointing
becomes more and more negative as
up.)
it accelerates downward.
This is a graph of x vs. t for an object moving with constant velocity.
The velocity is the gradient of the graph. Calculate the velocity. Velocity = 11/1.0 = 11 ms-1
This is a graph of velocity vs. time for an object with varying velocity;
The acceleration = gradient of the graph distance travelled = Area under graph
Describe motion in words. 1. Acceleration
2. Constant speed
3. Deceleration
4. Constant speed
Calculate: 1. Acceleration 2. Distance
For each section
Calculating Instantaneous velocity
Velocity = gradient of the tangent
Average Velocity Speed: how far an object travels in a given time interval
Velocity includes directional information:
Veloc ity ms-1 10
10
20
25
32
Time (s)
-10
CALCULATE AVERAGE SPEED AND AVERAGE VELOCITY
ACCELERATION Acceleration is the rate of change of velocity.
ACCELERATION Acceleration is a vector In one-dimensional motion we only need the sign. This is negative acceleration:
vf
vi
t
Gradient = vf – vi / t = a vf = vi + at
vf
vi
t
area = 0.5 (vf – vi) x t + vi x t = d vf - vi = at d= 0.5 (at) x t + vi x t = vit + 0.5at2
MOTION AT CONSTANT ACCELERATION Combining these equations allows us to develop 5 equations each with 4 variables vf = vi +at d= vit + 0.5at2 vf2 = vi2 + 2ad d = (vf +vi)t / 2 d = vf t – 0.5at2
Each equation has one missing variable out of the 5 used (d, vi, vf, a, t)
SOLVING PROBLEMS 1. Read the whole problem and make sure you understand it. Then read it again. 2. Write down the known (given) quantities, and then the unknown ones that you need to find 3. What physics applies here? Plan an approach to a solution.
SOLVING PROBLEMS 4. Which equations relate the known and unknown quantities? Are they valid in this situation? Solve algebraically for the unknown quantities, and check that your result is sensible (correct dimensions). 5. Calculate the solution and round it to the appropriate number of significant figures.
SOLVING PROBLEMS 6. Look at the result – is it reasonable? Does it agree with a rough estimate?
7. Check the units again.
FALLING OBJECTS Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity. This is one of the most common examples of motion with constant acceleration.
FALLING OBJECTS
In the absence of air resistance, all objects fall with the same acceleration, although this may be hard to tell by testing in an environment where there is air resistance.
FALLING OBJECTS
The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s2.
Summary • Kinematics is the description of how objects move with respect to a defined reference frame. • Displacement is the change in position of an object. • Average speed is the distance traveled divided by the time it took; average velocity is the displacement divided by the time. • Instantaneous velocity is the limit as the time becomes infinitesimally short.
Summary • Average acceleration is the change in velocity divided by the time. • Instantaneous acceleration is the limit as the time interval becomes infinitesimally small. • The equations of motion for constant acceleration are given, there are five, each one of which requires a different set of quantities. • Objects falling (or having been projected) near the surface of the Earth experience a gravitational acceleration of 9.80 m/s2.
