How fast can you walk?
Objective: Measure your personal walking speed.
Materials: Meter Stick / Any measuring device
Stopwatch / Cellphone with stopwatch
Procedure: Look for a straight path that you can freely walk.
: Mark the origin and the end point.
: Use a stopwatch to obtain the time it takes for you to walk a 20 m distance.
: Make 5 trials.
: Speed can be obtained by dividing the distance over time.
TRIALS DISTANCE ( m ) TIME ( S ) SPEED ( m/s )
1 20 20.40 1.0 m/s
2 20 18.94 1.0 m/s
3 20 18.17 1.1 m/s
4 20 17.21 1.2 m/s
5 20 16.40 1.2 m/s
speed = 1.1 m/s
20/1.1=18.2 m/s average speed
Analysis:
1.) Using your average speed, how far can you walk in 1 hour about 500 m. Look your average speed, how long it takes you from going these?
Miyerkules, Pebrero 6, 2013
Biyernes, Enero 25, 2013
PROBLEMS
1.Assuming that the world record for the 100-m dash is about 10 s, how fast are humans capable of running in m/s?Can you change this speed to miles per hour? (There are 1609 m in 1 mi, and 3600 s in 1 h)
22.37 mi/h
2.What is the acceleration of a vehicle that changes its velocity from 100 km/h to a dead stop in 10 s?
You can use the kinematics equation vf-vi=at
a=(vf-vi)/t
*(0-100)/10=10 in units of km/(hr*s)
3.A ball is thrown straight up with an initial speed of 30 m/s.How high does it go,and how long is it in the air (neglecting air resistance)
High=45.92 meters
Long=3.061 seconds
4.A ball is thrown with enough speed straight up so that it is in the air several seconds.
a.What is the velocity of the ball when it gets to its highest point?
zero
b.What is its velocity 1 s before it reaches its highest point?
one second before reaching the top,it is moving up at v=10 m/s
c.What is the change in its velocity during this 1 s interval?
dv=9.8 m/s
d.What is its velocity 1 s after it reaches its highest point?
v=9.8 m/s
e.What is the change in velocity during this 1 s interval?
dv=9.8 m/s
f.What is the change in velocity during the 2 s interval?
dv=18.6 m/s
g.What is the acceleration of the ball during any of these time intervals and when it passes through the zero velocity point?
At any point acceleration is a=9.8 m/s/s
5.What is the instantaneous velocity of a freely falling object 10 s after it is released from a position of rest? What is its average velocity during this 10 s interval?How far will it go during this time?
average velocity=49 m/s
i.velocity=98 m/s
distance=490 meters
6.A climber near the summit of a vertical cliff accidentally knocks loose a large rock.She sees it shatter at the bottom of the cliff 8 s later.What was the speed of impact?How far did the rock fall?
Far: 313.92 meters
final speed: 78.4 m/s for 8 seconds
7.A car goes from v=0 to v=50 m/s in 10 s.If you wish to find the distance traveled using the equation d=1/2at2,what value should you use for a?
a=5 m/s2
8.Consider a planet where the acceleration due to gravity is 20 m/s2.How fast and how far will an object at rest freely fall in 1 s?Compared to earth,how much greater and farther are the speed and distance fallen on this planet at given times?
10 m/s2.
20 m/s2
9.Surprisingly,very few athletes can jump more than 2 feet (0.6 m) straight up.Use d=1/2at2 and solve for the time one spends moving upward in a 2-foot vertical jump.Then double it for the "hang time"-the time one's feet are off the ground.
t=0.1625 seconds
hang time=0.403 seconds
10.Calculate the vertical height of Michael Jordan's jump when he attains a hang time of a full 1 s.
4.9meters
1.Assuming that the world record for the 100-m dash is about 10 s, how fast are humans capable of running in m/s?Can you change this speed to miles per hour? (There are 1609 m in 1 mi, and 3600 s in 1 h)
22.37 mi/h
2.What is the acceleration of a vehicle that changes its velocity from 100 km/h to a dead stop in 10 s?
You can use the kinematics equation vf-vi=at
a=(vf-vi)/t
*(0-100)/10=10 in units of km/(hr*s)
3.A ball is thrown straight up with an initial speed of 30 m/s.How high does it go,and how long is it in the air (neglecting air resistance)
High=45.92 meters
Long=3.061 seconds
4.A ball is thrown with enough speed straight up so that it is in the air several seconds.
a.What is the velocity of the ball when it gets to its highest point?
zero
b.What is its velocity 1 s before it reaches its highest point?
one second before reaching the top,it is moving up at v=10 m/s
c.What is the change in its velocity during this 1 s interval?
dv=9.8 m/s
d.What is its velocity 1 s after it reaches its highest point?
v=9.8 m/s
e.What is the change in velocity during this 1 s interval?
dv=9.8 m/s
f.What is the change in velocity during the 2 s interval?
dv=18.6 m/s
g.What is the acceleration of the ball during any of these time intervals and when it passes through the zero velocity point?
At any point acceleration is a=9.8 m/s/s
5.What is the instantaneous velocity of a freely falling object 10 s after it is released from a position of rest? What is its average velocity during this 10 s interval?How far will it go during this time?
average velocity=49 m/s
i.velocity=98 m/s
distance=490 meters
6.A climber near the summit of a vertical cliff accidentally knocks loose a large rock.She sees it shatter at the bottom of the cliff 8 s later.What was the speed of impact?How far did the rock fall?
Far: 313.92 meters
final speed: 78.4 m/s for 8 seconds
7.A car goes from v=0 to v=50 m/s in 10 s.If you wish to find the distance traveled using the equation d=1/2at2,what value should you use for a?
a=5 m/s2
8.Consider a planet where the acceleration due to gravity is 20 m/s2.How fast and how far will an object at rest freely fall in 1 s?Compared to earth,how much greater and farther are the speed and distance fallen on this planet at given times?
10 m/s2.
20 m/s2
9.Surprisingly,very few athletes can jump more than 2 feet (0.6 m) straight up.Use d=1/2at2 and solve for the time one spends moving upward in a 2-foot vertical jump.Then double it for the "hang time"-the time one's feet are off the ground.
t=0.1625 seconds
hang time=0.403 seconds
10.Calculate the vertical height of Michael Jordan's jump when he attains a hang time of a full 1 s.
4.9meters
EXERCISES
1.A ball is rolling across the top of a billiard table and slowly rolls to a stop.How would Aristotle interpret this observation?How would Galileo interpret this?
Galileo would say that the ball comes to rest because the ball seek its natural state to rest.Aristotle would likely have said it comes to rest because of some forces acting on it; likely friction between the ball and table surface and with the air.
2.Why did Galileo used inclined planes to investigate free fall?
Galileo spent a lot of time polishing the ramps he used in his gravity experiments, to minimize variance from friction.
3.Which has the greater average speed during a game: a football, a baseball, or a golf ball? Defend your answer.
A golf ball because it flew freely in the air without friction after it was hit!
4.One airplane travels due north at 300 km/h while another travels due south at 300 km/h.Are their speeds the same? Are their velocities the same? Explain.
The same speed but different velocities because it is on different directions.
5.Charlie drove his car around the block at constant velocity.True or false?Explain.
False because it could move at constant speed but not of constant velocity due to its ever changing direction.
6.Cite an example of something that undergoes acceleration while moving at constant speed.Can you also gave an example of something that accelerates while traveling at constant velocity?Explain.
Earth, constantly accelerating but moving at constant speed.
Sound, accelerates while traveling at constant velocity
7.Can you give an example wherein the acceleration of a body is opposite in direction to its velocity? Do so if you can.
Twanging a stretched rubber band
8.If you were standing in an enclosed car moving at constant velocity,would you have to lean in some special way to compensate for the car's motion?What if the car were moving with unchanging acceleration?Explain.
No because the velocity does not change so is the speed.My travel is so smooth.
9.On which of these hills does the ball toil down with increasing speed and decreasing acceleration.?
Hill number 2.
10.What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 seconds? Explain your answer.
Acceleration is a measure how much the speed is getting faster or slower.In this case the car is not getting faster or slower so the acceleration is zero.
11.For a freely falling object dropped from rest, what is its acceleration at the end of the 5th second of fall? The 10th second? Defend your answer.First acceleration due to gravity on earth is 9.8 m/s^2(32.2f/s^2) so
v=ta
v=5(9.8)
v=49 m/s
v=ta
v=10(9.8)
v=98 m/s
No matter what specific time you have,the acceleration will always be 9.8 m/s^2 due to earths gravity (unless acted upon by an outside force). So the answer to all the question is 9.8 m/s^2.
12.Suppose that a freely falling object were somehow equipped with a speedometer.By how much would its speed reading increase with its second of fall?
Each second it would get 9.8 m/s^2 faster since the acceleration due to gravity is 9.8 m/s^2.
13.Suppose that the freely falling object in the preceding exercise were also equipped with an odometer.Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds?Explain.
Different.As the speed increases the distance travelled per unit unit of time also increase.
14.When a ball player throws a ball straight up, by how much does the speed of the ball decrease each second while ascending( assume air resistance can be neglected)?By how much does it increase each second while descending?How much time is required for rising compared to falling?
The only force acting on the ball in either case is ( assuming no wind resistance as you state in the problem ) is gravity.
Acceleration (going down)=decceleration (going up) at approx. 9.8 m/s^2
So it will take the same amount of time to fall once it reaches the top as it will to get there and the speed when it returns to the height of the players hand again will be the same initial speed he threw it upwards in the first place.
15.Someone standing at the edge of a cliff throws a ball straight up at a certain speed and another ball straight down with the same initial speed.If air resistance is negligible,which ball will have the greater speed when it strikes the ground below?Explain.
Both hit with the same speed because the both hit the terminal velocity
16.If you drop an object,its acceleration toward the ground is 9.8 m/s2.
If you throw it down instead.would its acceleration after throwing be greater than 9.8 m/s2? Why or why not?
The object would still be accelerating at 9.8 m/s2 but its velocity would be greater due to the force from throwing.Once an object left your hand after being thrown, there is no more acceleration from the arm.
17.In the preceding exercise can you think of a reason why the acceleration of the object thrown downward through the air would actually be less than 9.8 m/s2?
If we consider air friction then the acceleration of an object in free fall is always less than 9.8 m/s2
18.If it will not by air resistance, why would it be dangerous to go outdoors on rainy days?
I think you would not received serious injury,a raindrop does not have enough mass to gain kinetic energy high enough to do more damage than large hail stones.
19.Extend tables 2.2 and 2.3 (which gives values of from 0 to 5 s) to 0 to 10 s, assuming no air resistance.
Time Velocity Distance Fallen
(seconds) ( m/s) (meters)
0 0 0
1 10 5
2 20 20
3 30 45
4 40 80
5 50 125
6 60 180
7 70 245
8 80 320
9 90 405
10 100 500
t (10)t (1/2)(10)t2
20.In this chapter,we studied idealized cases of balls rolling down smooth planes and objects falling with no air resistance.If a classmate complains that all this attention focused on idealized cases is valueless because idealized cases simply dont occur in the everyday world,how would you respond?How do you suppose tha author of this book would respond?
The motion of idealized system is far easier to understand.Once that motion is understood--as a first approximation--the motion with friction (such as air resistance) is then easier to understand as a refinement to the first approximation.
1.A ball is rolling across the top of a billiard table and slowly rolls to a stop.How would Aristotle interpret this observation?How would Galileo interpret this?
Galileo would say that the ball comes to rest because the ball seek its natural state to rest.Aristotle would likely have said it comes to rest because of some forces acting on it; likely friction between the ball and table surface and with the air.
2.Why did Galileo used inclined planes to investigate free fall?
Galileo spent a lot of time polishing the ramps he used in his gravity experiments, to minimize variance from friction.
3.Which has the greater average speed during a game: a football, a baseball, or a golf ball? Defend your answer.
A golf ball because it flew freely in the air without friction after it was hit!
4.One airplane travels due north at 300 km/h while another travels due south at 300 km/h.Are their speeds the same? Are their velocities the same? Explain.
The same speed but different velocities because it is on different directions.
5.Charlie drove his car around the block at constant velocity.True or false?Explain.
False because it could move at constant speed but not of constant velocity due to its ever changing direction.
6.Cite an example of something that undergoes acceleration while moving at constant speed.Can you also gave an example of something that accelerates while traveling at constant velocity?Explain.
Earth, constantly accelerating but moving at constant speed.
Sound, accelerates while traveling at constant velocity
7.Can you give an example wherein the acceleration of a body is opposite in direction to its velocity? Do so if you can.
Twanging a stretched rubber band
8.If you were standing in an enclosed car moving at constant velocity,would you have to lean in some special way to compensate for the car's motion?What if the car were moving with unchanging acceleration?Explain.
No because the velocity does not change so is the speed.My travel is so smooth.
9.On which of these hills does the ball toil down with increasing speed and decreasing acceleration.?
Hill number 2.
10.What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 seconds? Explain your answer.
Acceleration is a measure how much the speed is getting faster or slower.In this case the car is not getting faster or slower so the acceleration is zero.
11.For a freely falling object dropped from rest, what is its acceleration at the end of the 5th second of fall? The 10th second? Defend your answer.First acceleration due to gravity on earth is 9.8 m/s^2(32.2f/s^2) so
v=ta
v=5(9.8)
v=49 m/s
v=ta
v=10(9.8)
v=98 m/s
No matter what specific time you have,the acceleration will always be 9.8 m/s^2 due to earths gravity (unless acted upon by an outside force). So the answer to all the question is 9.8 m/s^2.
12.Suppose that a freely falling object were somehow equipped with a speedometer.By how much would its speed reading increase with its second of fall?
Each second it would get 9.8 m/s^2 faster since the acceleration due to gravity is 9.8 m/s^2.
13.Suppose that the freely falling object in the preceding exercise were also equipped with an odometer.Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds?Explain.
Different.As the speed increases the distance travelled per unit unit of time also increase.
14.When a ball player throws a ball straight up, by how much does the speed of the ball decrease each second while ascending( assume air resistance can be neglected)?By how much does it increase each second while descending?How much time is required for rising compared to falling?
The only force acting on the ball in either case is ( assuming no wind resistance as you state in the problem ) is gravity.
Acceleration (going down)=decceleration (going up) at approx. 9.8 m/s^2
So it will take the same amount of time to fall once it reaches the top as it will to get there and the speed when it returns to the height of the players hand again will be the same initial speed he threw it upwards in the first place.
15.Someone standing at the edge of a cliff throws a ball straight up at a certain speed and another ball straight down with the same initial speed.If air resistance is negligible,which ball will have the greater speed when it strikes the ground below?Explain.
Both hit with the same speed because the both hit the terminal velocity
16.If you drop an object,its acceleration toward the ground is 9.8 m/s2.
If you throw it down instead.would its acceleration after throwing be greater than 9.8 m/s2? Why or why not?
The object would still be accelerating at 9.8 m/s2 but its velocity would be greater due to the force from throwing.Once an object left your hand after being thrown, there is no more acceleration from the arm.
17.In the preceding exercise can you think of a reason why the acceleration of the object thrown downward through the air would actually be less than 9.8 m/s2?
If we consider air friction then the acceleration of an object in free fall is always less than 9.8 m/s2
18.If it will not by air resistance, why would it be dangerous to go outdoors on rainy days?
I think you would not received serious injury,a raindrop does not have enough mass to gain kinetic energy high enough to do more damage than large hail stones.
19.Extend tables 2.2 and 2.3 (which gives values of from 0 to 5 s) to 0 to 10 s, assuming no air resistance.
Time Velocity Distance Fallen
(seconds) ( m/s) (meters)
0 0 0
1 10 5
2 20 20
3 30 45
4 40 80
5 50 125
6 60 180
7 70 245
8 80 320
9 90 405
10 100 500
t (10)t (1/2)(10)t2
20.In this chapter,we studied idealized cases of balls rolling down smooth planes and objects falling with no air resistance.If a classmate complains that all this attention focused on idealized cases is valueless because idealized cases simply dont occur in the everyday world,how would you respond?How do you suppose tha author of this book would respond?
The motion of idealized system is far easier to understand.Once that motion is understood--as a first approximation--the motion with friction (such as air resistance) is then easier to understand as a refinement to the first approximation.
Huwebes, Enero 24, 2013
Free Fall
How Fast
22. What exactly is meant by a freely falling object?
23.What is the gain in speed per second for a freely falling object?
24. What is the velocity acquired by a freely falling object 5 s after being dropped from a rest position? What is it 6 s after?
25.The acceleration of free fall is about 10 m/s2, Why does the seconds unit appear twice?
How Fast
22. What exactly is meant by a freely falling object?
23.What is the gain in speed per second for a freely falling object?
24. What is the velocity acquired by a freely falling object 5 s after being dropped from a rest position? What is it 6 s after?
25.The acceleration of free fall is about 10 m/s2, Why does the seconds unit appear twice?
Acceleration
15. Distinguish between velocity and acceleration.
Velocity-the speed and the direction of motion
Acceleration-the rate of change in velocity
16.What is the acceleration of a car that increases its velocity from 0 to 100 km/h in 10 s?
10 km/h in 10 seconds
17.What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 s?
10 km/h in 1 seconds
18.When does one feel the effects of velocity in a moving vehicle when it is moving uniformly or when motion changes?
when moving uniformly
19. Acceleration is generally defined as the time rate of change of velocity.When can it be defined as the time rate of change of speed?
when there is no change of velocity.
15. Distinguish between velocity and acceleration.
Velocity-the speed and the direction of motion
Acceleration-the rate of change in velocity
16.What is the acceleration of a car that increases its velocity from 0 to 100 km/h in 10 s?
10 km/h in 10 seconds
17.What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 s?
10 km/h in 1 seconds
18.When does one feel the effects of velocity in a moving vehicle when it is moving uniformly or when motion changes?
when moving uniformly
19. Acceleration is generally defined as the time rate of change of velocity.When can it be defined as the time rate of change of speed?
when there is no change of velocity.
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