Kinematics – study of the motion of objects using words ...



KINEMATICS LESSON 1

Kinematics – study of the motion of objects using words, diagrams, numbers, graphs, and equations.

Language of Kinematics:

• Scalars a quantity having magnitude (or numerical value) and unit only.

• Vectors a quantity having both a magnitude, unit and a direction. (has arrow above letter, v verses v)

Symbol Term Scalar Vector Units

d distance yes meters (m), kilometers (km),

miles (mi.)

d displacement yes 6 m, South

(change in position)

v speed yes m/s, km/h, mi/h

v velocity yes 4 m/s, North

a acceleration yes 2 m/s2, East

m mass yes grams(g), kilograms(kg),

pounds (lb)

F force yes N (Newtons) = km*m/s2

W Work yes J (Joules) = N*m

P Power yes W (Watts) = J/s

p Momentum yes kg*m/s, down

Which of the following quantities are vector or scalar?

50 km/h 20 m/s, South

6 km, N 400 N, down

800 kg 200 centuries

DISTANCE VS DISPLACEMENT

Distance and Displacement seem like the same thing but

• Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.

• Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

Confused??

I walk 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

[pic]

What is my displacement?

When I am finished walking, I am not "out of place" - i.e., there is no displacement for my motion (displacement = 0 m).

What is my total distance? I covered 12 meters of ground

QUESTION - What is your displacement if you begin at the school, run 10 kilometers and finish 20 meters North of the school? What is the distance you covered?

ANSWER - displacement = 20 m, North, distance = 10 kilometers

SPEED AND VELOCITY

We often use the words speed and velocity interchangeably.

However,

• speed is a scalar quantity -- "how fast an object is moving"

• velocity is a vector quantity -- " the rate at which an object changes its position"

Going back to my trip, if I return to my original position, I have not moved from my original position and therefore I have no velocity. However, during the time I was moving, I had a speed.

Speed is the rate at which a distance is covered and is measured in terms of distance traveled over a given period of time.

SPEED = change in distance = Δ d

change in time Δ t

Measured in km/h, km/s, m/h, m/s …

AVERAGE SPEED

During a typical trip to school, your car will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often.

The speedometer of a car reveals information about the instantaneous speed of your car. It shows your speed at a particular instant in time.

 

[pic]

 

The instantaneous speed of an object is not to be confused with the average speed.

Average speed is a measure of the distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio. Suppose that during your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The average speed of your car could be determined as

[pic]

 

On the average, your car was moving with a speed of 25 miles per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 miles per hour. Yet, on average, you were moving with a speed of 25 miles per hour

During any trip, a car's speed varies, so we calculate its average speed.

Average Speed = total distance travelled

travel time

VELOCITY

A VELOCITY quantity = 60 km/h to the north

Driving in your car you are concerned about your speed - how fast you are going.

Speed = distance/time

An airplane pilot is concerned with velocity - how fast he is going and in what direction.

Velocity = speed and direction

Airplanes tend to travel in straight lines from Point A to Point B as the crow flies, therefore they measure velocity which is a difference in their displacement over time.

velocity = Δ d = df – di

Δ t tf - ti

INSTANTANEOUS VELOCIY is the same as instantaneous speed but with direction.

CONSTANT VELOCITY is very different than CONSTANT SPEED.

Constant Velocity is Constant Speed with no change in direction.

A car can round a curve with a constant speed, but can the car have a constant velocity?

What part of the velocity is changing?

ACCELERATION

ACCELERATION is a vector quantity that defines a rate of change in velocity.

When velocity is constant, there is no acceleration.

Examples of acceleration?

“Car hits the accelerator and then brakes to a stop on a straightstretch”

Example of change in speed but not direction

“Car drives at a constant speed around a track”

Example of change in direction but not speed

“Rollercoaster”

Example of change in speed and direction

Anyone who has stood in a bus has experienced the difference between velocity and acceleration. You can stand with little difficulty in a bus that moves with constant velocity, it is only if the bus accelerates -- speeds up, slows down or turns a corner -- that you experience difficulty.

Acceleration = change of velocity = vfinal - vinitial = Δ v

Time interval t t

What is the acceleration of the car?

0km/h -----------( 60 km/h in 3 seconds

3 seconds x 1min x 1 hour= 0.000833 hours

60s 60min

Acceleration =vfinal - vinitial=60 km/h - 0 km/h =7 x 103 km/h2

t 0.00833 h

Units of acceleration are velocity units divided by time units m/s2, km/h2 …

The general RULE OF THUMB is:

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

Deceleration is a negative acceleration, - 20 m/s2.

When the motorcycle decelerates, what is its acceleration?

30 km/h -------------------------( 0 km/h in 5 seconds

5 seconds x 1min x 1 hour= 0.00139

60s 60min

Acceleration=vfinal - vinitial=0 km/h - 30 km/h =-2 x 104 km/h2

t 0.00139 h

The above examples are of constant acceleration, however, not all things accelerate constantly.

Computer Demo

DESCRIBING MOTION WITH DIAGRAMS

TICKER TAPE DIAGRAMS

Imagine driving a car that has a bucket of paint with a hole in it attached to your bumper.

What would happen to the paint drops on the pavement as you speed up?

Slowed down?

Went a constant speed?

Stopped?

The paint spots on the pavement tell a story about your movement!

In the lab, we will be using ticker tape diagrams (similar to our paint drops) to measure velocity and acceleration of a cart's movement

A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time - say every 0.1 second. As the object moves, it drags the tape through the "ticker," thus leaving a trail of dots.

[pic]

[pic]

[pic]

VECTOR DIAGRAMS

Vector Diagrams use arrows to show speed and direction.

[pic]

Since the arrows are the same length and in the same direction, the velocity is constant.

[pic]

In the future, vector diagrams will be used to describe direction and magnitude of acceleration, force and momentum.

[pic]

KINEMATICS LESSON 1 PART 2

HOMEWORK

1. Categorize each quantity as being either a vector or a scalar.

m = meters

s = seconds

km = kilometers

kg = kilograms

h = hours

a. 8 m

b. 30 m/s, East

c. 2 miles, North

d. 20 m/s

e. 6 km

f. 25 kg

g. 60 km/h

h. 3 m/s2, Southeast

2. What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school?

3. The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes. Then click the button to see the answer.

 

[pic]

4. A football coach paces back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D.

What is the coach's resulting displacement and distance of travel? Click the button to see the answer.

[pic]

5. What is the average speed of a cheetah that sprints 100.0 m in 4.0 seconds? How about if it sprints 50.0 m in 2.0 s?

6. If a car moves with an average speed of 60.0 km/h for an hour, it will travel a distance of 60.0 km.

a. How far would it travel if it moved at this rate for 4 hours?

b. For 10 hours?

c. Would it be possible for the car that starts from rest to attain an average speed of 60 km/h and never exceed a reading of 60 km/h on the speedometer?

7. "She moves at a constant speed in a constant direction." Say the same sentence in fewer words.

8. The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

9. During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?

10. What is the velocity of an airplane that flies 602 m [East] in 2.50 s?

11. A spaceship traveled at 2.1 x 106 km in 2.7 days. What was the velocity of the spaceship in km/days and km/h?

12. A person walks 5.0 km towards the east in 2 hours, then 1.5 km towards the west in 0.50 hours, and finally 10.0 km towards the east again in 2.25 hours. What is the person's average velocity? I recommend drawing a diagram.

13. A particular car can go from rest to 90.0 km/h in 10.0 s. What is its acceleration?

14. In 2.5 s a car increases its speed from 60.0 km/h to 65 km/h while a bicycle goes from rest to 5.0 km/h. Which undergoes the greater acceleration? What is the acceleration of each vehicle?

15. A car decelerates at 2.0 m/s2. If the car's initial velocity is 40.0 m/s [East], what is its final velocity 3.5 s later? Just plug in the numbers into the acceleration equation and solve for vfinal.

16. A car accelerates at -2.0 m/s2. If its initial velocity is 24 m/s [West], what will its velocity be 8.0 s later?

17. Describe the motion of the following ticker tape diagrams.

a. [pic]

b. [pic]

c. [pic]

Answer Key

1. No Answer Key

2. No Answer Key

3. 140 m, rightward

4. 55 yards, left

5. 25 m/s, 25 m/s

6. 240 km, 600 km, No, explain

7. No Answer Key

8. No Answer Key

9. No Answer Key

10. 241 m/s, East

11. 3.2 x 104 km/h

12. 2.8 km/h [East]

13. 3.24 x 104 km/h2

14. 7.2 x 103 km/h2, 7.2 x 103 km/h2

15. 33 m/s [E]

16. 8.0 m/s [W]

17. No Answer Key

KINEMATICS LESSON 1 PART 2

HOMEWORK

1. Categorize each quantity as being either a vector or a scalar.

m = meters

s = seconds

km = kilometers

kg = kilograms

h = hours

i. 8 m

j. 30 m/s, East

k. 2 miles, North

l. 20 m/s

m. 6 km

n. 25 kg

o. 60 km/h

p. 3 m/s2, Southeast

a. scalar b. vector c. vector d. scalar e. scalar f. scalar g. scalar h. vector

2. What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school?

Answer: Displacement is 0 as they are not displaced from the school.

3. The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes.

 

[pic]

Answer:

The skier covers a distance of

(180 m + 140 m + 100 m) = 420 m

and has a displacement of 140 m, rightward.

4. A football coach paces back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D.

What is the coach's resulting displacement and distance of travel?

[pic]

Answer:

The coach covers a distance of

(35 yds + 20 yds + 40 yds) = 95 yards

and has a displacement of 55 yards, left.

5. What is the average speed of a cheetah that sprints 100 m in 4 seconds? How about if it sprints 50 m in 2 s?

Average speed = 100 m / 4 s = 25 m/s

Average speed = 50 m / 2s = 25 m/s

6. If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km.

d. How far would it travel if it moved at this rate for 4 hours?

Distance = 60 km x 4 hours = 240 km

Hour

e. For 10 hours?

Distance = 60 km x 10 hours = 600 km

Hour

f. Would it be possible for the car that starts from rest to attain an average speed of 60 km/h and never exceed a reading of 60 km/h on the speedometer?

No, since the speed was below 60 km/h, 0 ( 60 km/h, the car needs to exceed 60km/h to average out to 60 km/h over the trip.

7. "She moves at a constant speed in a constant direction." Say the same sentence in fewer words.

She moves with a constant velocity.

8. The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

Both cars have the same speed.

The cars do not have the same velocity since they are moving in opposite directions.

9. During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?

This indicates a constant speed, but probably not a constant velocity unless the car is traveling in only one direction over that period of time.

10. What is the velocity of an airplane that flies 602 m [East] in 2.50 s?

Velocity = 602 m / 2.50 s = 240.80 m/s [East]

11. A spaceship traveled at 2.1 x 106 km in 2.7 days. What was the velocity of the spaceship in km/days and km/h?

Velocity = 2.1 x 106 km / 2.7 days = 7.8 x 105 km/days

7.8 x 105 km x 1 day = 3.2 x 104 km/h

days 24 hours

12. A person walks 5.0 km towards the east in 2 hours, then 1.5 km towards the west in 1/2 hour, and finally 10.0 km towards the east again in 2.25 hours. What is the person's average velocity? I recommend drawing a diagram.

Average velocity = displacement = 5.0 km east + 10 km east – 1.5 km west

Time ( 2 + 0.5 + 2.25) hours

Average velocity = 13.5 km [East]/4.75 hours = 2.84 km/h [East]

13. A particular car can go from rest to 90 km/h in 10 s. What is its acceleration?

Acceleration = 90km/h = 9 km/h/s OR 9 km/h*s

10 s

14. In 2.5 s a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. Which undergoes the greater acceleration? What is the acceleration of each vehicle?

Acceleration = vf - vi = Δ v

Δ t Δ t

Car’s Acceleration = 65 km/h – 60 km/h = 2 km/h*s

2.5 s

Bicycle’s Acceleration = 5 km/h – 0 km/h = 2 km/h*s

2.5 s

Yes, the accelerations are the same.

15. A car decelerates at 2.0 m/s2. If the car's initial velocity is 40 m/s [East], what is its final velocity 3.5 s later? Just plug in the numbers into the acceleration equation and solve for vfinal.

Acceleration = vf - vi

Δ t

negative sign because the car is decelerating

-2.0 m/s2 = vf – 40 m/s [E]

3.5 s

-7.0 m/s = vf – 40 m/s [E]

vf = 33 m/s [E]

16. A car accelerates at -2.0 m/s2. If its initial velocity is 24 m/s [West], what will its velocity be 8.0 s later?

Acceleration = vf - vi

Δ t

-2.0 m/s2 = vf – 24 m/s [W]

8.0 s

-16.0 m/s = vf – 24 m/s [W]

vf = 8.0 m/s [W]

17. Describe the motion of the following ticker tape diagrams.

d. [pic]

Object is slowing down (decelerating), then stops, then accelerates.

e. [pic]

Object is moving with a constant velocity and then accelerates.

f. [pic]

Object is moving with a constant velocity, decelerates, comes to a stop and then continues with a constant velocity.

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