Speed and Velocity

Click to move to the next page or to go to the previous page. Click underlined words for links to

explanations.

Resources-

Science Voyages, Level Blue, Glencoe/McGraw-Hill, 2000

Science Interactions, Course 1, Glencoe, 1993

Motion, Forces, and Energy, Prentice Hall, 1993

If instructed to do so, please complete the worksheet for this

presentation.

This is your vocabulary-

• position

• reference point

• motion

• distance

• SI

• meter

• unit

• time

• speed

• speedometer

• odometer

• displacement

• velocity

• relative

• frame of reference

• average

• constant

• instantaneous

These are your formulas-

Speed =Distance

Time

Velocity =Displacement

Time

So, where are you?You and your friend agree to meet for a movie tonight. You decide to get together at the corner of Lee and 3rd Streets in 30 minutes.

Where you will meet is the position as described by a reference point. A reference point is an object that does not move.

The time you will meet is measured with a clock. Time is defined as the interval between two events (when you make the decision to meet and when you meet). Over the years, time has been measured with sundials, hour glasses, watches, and the most accurate clock, the atomic clock.

Click the object for a history of clocks

As you walk to meet your friend, you change your position with every step you take. Distance is how far you travel

along a path while you change your position.

Distance is measured in units. This is a system ofmeasurement that scientists all over the world use so they can

communicate information clearly. SI stands for the International System of Units called the metric system, a system based on the

number ten. The basic unit of length is the meter (m).

Do you want to know more about units of length and the metric system?

Visit these links Metric System SI Metric Numbers How Many?

While you were walking to meet your friend, you were in motion. Changing position creates motion.

You have gone a distance, and time has passed while you were changing your position.

O.K. Just how fast are you moving?

To be able to meet your friend on schedule, you had to go a distance in a certain time. Speed is the distance traveled by an object during a given time interval (distance divided by time) .

You stop for a few minutes to watch a ball game at a local park, hurry to cross the street, and rush to get there on time. You do not maintain a constant speed. Even if your speed isn’t constant, you can find your average speed by using this equation---

Speed =Time =Distance

average speed = total distancetime interval

A cheetah can maintain a constant speed for short periods of time. Its speed is the same at all times during its motion. In 4 minutes, the cheetah traveled 8 km.

speed = 8 km4 min

= 2 km/min

0 1 2 3 4

Most objects do not move at constant speeds for very long. Dividing the total distance by the total time does not tell you the speed for every point of the journey. Instead it gives you the average speed.

The rabbit had a burst of speed during the second minute. What is going on between the 3rd and 4th minutes?

0 1 2 3 4 Time

Time

Answer

The rabbit is not moving. Time passes but no distance is covered.

Distance

Distance

v = 2 km/min t = 4 min

d = 8 km

Let’s put a move that formula-

Suppose you were given the speed and the time. Could you determine the distance?

This time you know the distance and the speed. Can you find out how long it took for the cheetah to go the distance?

Yes. d = v t

Yes. t = d / v

Instantaneous speed-Instantaneous speed is the rate of motion at any given instant. What does that mean?

The picture at the right gives you the speed of the runner at the instant the picture was taken.

8.5 meters/second

The speedometer in your car gives you a reading of instantaneous speed.

While the speedometer is showing the speed at any given moment, the odometer shows you how far you have gone. An odometer measures distance.

00566

76767

6

500 km

Distance = speed x time

Let’s work a problem or three-

A car travels 240 km in 3 hours. What is the speed of the car during that time?

80 km/hr

Speed = Distance/TimeCheck for your answer

The speed of a ship is 50 km/hr. How far will it travel in 10 hours? (Something different here!)

Check for your answer

A friend lives 4 km away. Walking at 2 km/hr, how long will it take you to go this distance? (Be careful---it’s another version of the formula!)

Check for your answer 2 hrs

time = distance/speed

Let’s talk displacement-Have you ever ridden a roller coaster? You twist and turn for three or four minutes, but you get on and off at the same place. Even with all the turns, you really haven’t gone anywhere at all.

Displacement is the change in position of an object. If you end up where you started, your displacement is zero.

Displacement is described by both a length and a direction. Distance is described only by length. To say that you live 6 km from the amusement park isn’t very helpful unless you state in which direction (6 km south).

Velocity

When you know the speed and direction of an object’s motion, you

know the velocity of the object.

For example, the meteorologist (one who studies the weather) gives the velocity of the wind.

The wind is out of the southwest at 10 km/hr.

Velocity is the displacement of an object divided by time.

The formula for velocity is-

Velocity =Displacement

Time

=

In the formula, v stands for average velocity and d for displacement. Time is t.

v =dt

Does it sound like speed and velocity are the same thing? How about distance and displacement?

You live 10 km away from school. There is a heavy snow. It took you 5 hours to walk to school. So, what is the distance you traveled?

Well, if you walked in a straight line, through houses, trees, and fences, it would be 10 km. But if one connected all your footprints

and measured the distance, it was actually 15 km.

The distance is 15 km. Your displacement is 10 km in the direction of the school. Your speed was 3 km/hr but your velocity was 2

km/hr in the direction of the school.

If you walk back home, your displacement is zero, and your velocity is 0 km/hr. Well, just think of it, all the years you walked to school

and back home your displacement and velocity were both zero!

15 km/ 5 hr = 3 km/hr (speed) 10 km/ 5 hr = 2 km/hr in the direction of the school (velocity)Click here to view how to do these problems.

Let’s work a problem or two-

An airplane is flying from Bridgeport, WV, to Washington, DC., a distance of 330 km. The trip takes 1.5 hours. What is the airplane’s velocity?

The total displacement divided by total time is a velocity of 220 km/hr east.Click here for the answer.

A girl walks 2 km west, she turns and walks 3 km east. What distance does she walk? What is her displacement?

The distance she walked 5 km. Her displacement is 1 km east.Click here for the answer.

Would the paper airplane’s distance traveled be the same as its velocity?

Suppose you are swimming downstream at 10 km/hr. You are actually going faster. How? The water is

moving at 10 km/hr. Since you are swimming downstream, both you and the river are going in the

same direction. The velocities combine (add). You are moving at 20 km/hr. What would happen if you were

swimming upstream against the flow of water?

Velocities must be in the same direction to add them. You must subtract when combining velocities in opposite

directions. You would be swimming at 0 km/hr or simply going nowhere!

10 km/hr downstream – 10 km/hr upstream = 0 km/hr

Click here for the answer.

Frame of reference-

When you describe something that is moving, you are comparing it with something that stationary or not moving. This stationary object is your frame of reference.

Think about an astronaut on a space walk. If you are the astronaut, the shuttle is your frame of reference (your relative velocity to the shuttle is zero). But, if you are on the ground, you would describe both the astronaut and the shuttle having a velocity of 40,000 km/hr. The Earth is your frame of reference.

Speed is defined as the distance traveled by an object in one unit of time.

Distance Time

Speed =

For example, if a car travels 50 kilometers in one hour, the car is traveling at a speed of 50 km/h. An ant moving two centimeters in one second

moves at a speed of two centimeters per second or 2 cm/s. The ant has a much slower speed.

Time is the interval (gap or break) between two events. It is a

quantity that is measured with a clock. A clock is designed to mark

off equal time intervals. The difference between two clock readings tells you how long

something takes and is called a time interval.

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