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Shedding Light on Motion

Episode 1:

Speed

The Shedding Light on Motion series is a visual treasure trove of demonstrations, animations, and explanations of

all things motion! To an extent we’re all familiar with motion because we all move and we see movement

everywhere, but a detailed knowledge of motion has allowed us to build the wonderful modern world that we live

in.

In Episode 1, Speed, presenter Spiro Liacos introduces students to the concept that speed is a measure of how far

something travels in a given amount of time, looks at how speed varies in a sprint, explains the concept of velocity,

and demonstrates a number of ways of measuring an object’s speed.

Contents:

Part A: Introduction.

Part B: How Fast? We explain the basic definition of speed, show how a sprinter’s speed varies in a race,

introduce SI units (and explain why there are 300 million good reasons to use them), and do some lightning fast

Mathematics (pun fully intended).

Part C: Converting Between m/s and km/hr. It’s amazing how far you travel in a single second when you’re in a

car, and even more amazing how quickly car crashes occur.

Part D: Measuring Speed. How fast can you kick a ball or ride a bike? We take a look at speedos, stopwatches,

cameras and more…

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Shedding Light on Motion Episode 1: Speed

The images shown below are screen grabs from the program and the text is more or less a transcript of the program.

Part A: Introduction

In this series, we’re going to look at motion and at the forces that cause

motion.

To an extent, we’re all familiar with motion

because we all move and we see movement

everywhere. However, without a detailed

study of motion and of forces, many of the

technological marvels that are now part of

our modern world just wouldn’t exist.

Let’s begin our study of motion by taking a look at the concept of speed.

Part B: How Fast?

Speed is basically how much distance you travel in a given amount of time. Speed can be measured in

metres/second, kilometres/hour, or in miles per hour. Like many of the concepts that we’re going to look at in this

series, it’s probably easiest to think of speed in mathematical terms.

speed = distance travelled / time taken

I can run 100 m in 15 seconds, so my average speed over a 100 m track is 6.7

metres per second. I can ride 100 m in 13 seconds, so my average speed on the

bike was 7.7 metres per second.

The two speeds I calculated over the 100m track were averages, of course. My

actual speed at any given moment varies.

Here we can see the whole 100m track. That little speck there is

me there dressed in bright orange so that you can see me a little

easier. By drawing dots on the screen of my position after 1

second, 2 seconds, 3 seconds and so on right up to the 15 second

mark when I crossed the finish line, you can see that the distance I

covered every second varied. As I got faster near the start, I

covered more distance every second. In the middle of the sprint I

was travelling more or less at the same speed, since I was

covering the same distance every second. Towards the end, I

slowed down a little and was covering less distance per second.

I can actually compare my 100m running sprint with my 100m bike

sprint. On the bike, I sped up quite slowly, but kept getting faster and

faster for a longer amount of time and my highest riding speed ended up

being much greater than my highest running speed. You can see that as a

runner I was in the lead for most of the race—here at the 8-second mark,

I as a runner was ahead—but after that I as a bike rider caught up, and

then passed my running self.

If I get some students to time me every five metres, I can get more information about how my actual speed changes

over a 100m sprint. Here are the times that I took to run 5 m, 10 m, 15 m, and so on. I’m only showing the first 50

metres here so that you’re not overloaded with information. I ran the first 5 m interval in 1.49 s, which means my

average speed in that 5 m interval was 5 m/1.49 s or 3.4 m/s. The next 5 m interval took me only 0.87 seconds

(2.36 s – 1.49 s), so my average speed during that time interval was 5 m/0.87 s which equals 5.7 m/s.

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We can repeat the procedure and get a good estimate of my speed

during each 5m interval. These are still only averages, but they give

a clearer indication of my actual speed at various points in the race.

At the start, I wasn’t moving, so I should fill in the zero, but then I

got faster and faster until I reached a constant speed of 8.1 m/s

(which is about 29 km/hr). After that I actually started slowing

down.

So, an object’s average speed is the overall distance it travels

divided by the time taken, but its “actual” or “instantaneous” speed is the speed at which the object is travelling at

any given instant.

A car’s speedometer indicates a car’s instantaneous speed. We’ll discuss speedometers in a little more detail soon.

In this amateur 100m race, the fastest runner ran the 100m race in 9.98 seconds. His average

speed was (100m over 9.98 seconds which equals) 10.02 m/s, but his highest speed was about

12 m/s.

We can actually display information about a runner’s position and speed in

graphs. These graphs are showing information about the 2009 world record

100 m sprint of Jamaican athlete Usain Bolt who ran the 100 in just 9.58

seconds. His average speed was 10.4 m/s (average speed = 100 m / 9.58 s),

but as you can see in the speed vs time graph, he reached a speed of about

12.1 m/s. Professional athletes often use data like this to work out their

strengths and weaknesses and to try improve their times. We’ll talk more

about graphing in Episode 4 of our series.

Now in these calculations, I’ve used metres, seconds, and metres per second as

my units. These units form part of what are called the SI units, some of

examples of which I’m showing here. They are the most widely used units

among scientists around the world. SI is short for the French Système

International d'Unités or in English the International System of Units. Having

a co-ordinated system of measurement allows scientists all around the world to

collaborate more effectively.

In 1998, NASA launched the Mars Climate Orbiter, which was meant

to go into orbit around Mars to study the Martian climate and

atmosphere. However, the different teams working on the different

parts of the orbiter’s guidance and propulsion systems didn’t all use

the same units. As a result, when the thrusters fired to slow it down

after its long journey from Earth, they didn’t fire for the correct

amount of time. The spacecraft passed too close to the planet, hit its

upper atmosphere and disintegrated. The total cost was about

US$330 million. Units are important! (And I still love NASA!)

Though m/s is the preferred unit for speed among scientists, we can still use

other units though. If a car travels 120 km in 2 hours, its average speed is

60km per hour. This is the unit used in most of the world for speed limits and

on car speedometers. The word kilometre is often just called a “k”. In the

UK and in the US, miles are typically used for distance. If you travel 180

miles in 4 hours, your average speed is 45 miles per hour. One mile = 1.6 km,

so for example 45 miles per hour = 72 km/hr. 50 miles per hour = 80 km/hr.

Now related to the concept of speed is the concept of velocity. Velocity is pretty much the same thing as speed but

an object’s velocity is the speed that it’s travelling at and the direction that it’s travelling in.

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Engineers designing a car’s engine for example have to take into account that, in this

case, while two of the pistons are moving upwards, the other two are moving downwards.

If we define upwards as positive, then when the pistons are moving upwards they have a

positive velocity, and when they’re moving downwards, they have a negative velocity. At

any given instant all the pistons are actually moving at the same speed, but pistons 1 and

4 have different velocities to pistons 2 and 3, since they’re moving in a different direction.

Both speed and velocity are measured in the same unit: metres per second.

These cars have a speed of about 80 km/hr. The cars at the bottom of the screen though have a velocity of 80

km/hr to the east, or if you like 80 km/hr to the right or even positive 80 km/hr, if we define movement to the right

as positive. The cars at the top of the screen have a velocity of 80 km/hr to the west, or 80 km/hr to the left, or even

negative 80 km/hr since we’ve defined movement to the right as positive. (The negative doesn’t mean the cars are

facing backwards. The expression -80 km/hr simply tells you the speed and the direction.)

So, velocity is basically speed and direction. It might seem kind of trivial, because in the early stages of studying

motion you might not care about an object’s direction. However, an incredible amount of mathematics goes into the

design of pretty much everything, and as we get more advanced, knowing an object’s speed and direction is very

useful. From now on I’m going to use the symbol v for both speed and velocity; (lowercase) v is the symbol used

by scientists all around the world.

The formula average speed = distance travelled over time taken can therefore be

written as

vave = d/t where vave = average speed or average velocity, d = distance and t = time.

Now a quick explanation of this subscript ave. It’s fairly common is Science to use a

quantity’s general symbol followed by a subscript which indicates a little more

information about the quantity. The symbol for force for example is F, so we might write Fgravity (F subscript

gravity) if we’re specifically talking about the force of gravity, or Fair resistance if we’re talking about the force of air

resistance. We might also write vcar if we’re referring to the velocity of a particular car. In this general formula, I’ve

used the ave to indicate that the velocity I’m talking about is an average velocity.

The formula can also be written simply as v = d/t if the object is actually moving at a constant speed, but I’m going

to use vave because it’s a little bit more general.

Moving on now, we can rearrange the formula to make distance the subject: distance = average speed x time d= vave

x t

For example, if you travel at a speed of 100 km/hr for 4 hours, you will cover a distance of, d = vave x t = 100 km/hr

x 4 hours = 400km.

However, what distance will you cover, if you run at a speed of 4m/s

for 30 minutes? The units have to be consistent, so we have to

convert 30 minutes into seconds. There are 60 seconds in a minute,

so 30 minutes equals 1800 seconds. The distance is therefore 4m/s x

1800s which equals 7,200metres, or 7.2 km.

So, metres, seconds and metres per second go together and

kilometres, hours and kilometres per hour go together. If a question

has mixed units, you’ll have to convert one of them

If you travel at 5 m/s for 20 seconds, the distance you cover is v x t, or 5 m/s x 20 s which equals 100 m.

If you travel at 5 m/s for 20 minutes, you will obviously cover much more distance. In this case, the minutes have

to be converted to seconds. 20 minutes = 20 x 60 seconds, or 1200 seconds. The distance therefore is 5 m/s x 1200

s, which equals 6000 m.

If you travel at 5 m/s for 20 hours you will obviously travel even further. Always be careful about the units!

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Now we can also rearrange the formula to make time our subject:

time = distance / speed

So, for example, how much time will it take to travel from Melbourne to Sydney

by road if the distance is 900km and I can travel at a speed of 100 km/hr? Quite

simply: 9 hours.

The best tennis players in the world serve the ball at about 200 km/hr (about 55 m/s), though their fastest serves

reach about 250 km/hr. Because of air resistance, the ball slows down really quickly after it’s struck and after it

bounces it slows down even more. The average speed that the ball travels on its way to the receiver is about 105

km/hr or about 30 m/s.

So, how much time does it take for a tennis ball travelling at an average speed of 30 m/s to travel 23.77 m, which is

the length of the court. Time = distance over average speed (t = d/vave) which equals 23.77 m / 30 m/s which equals

0.8 seconds. Professional tennis players have only about 0.8 seconds to work out where the ball is going, decide on

how they’re going to play it, get into position, and then actually play it! In this case, the serve was too fast and the

receiver couldn’t return the ball.

Light travels at an incredible 300 000 000 m/s, while sound travels at only

about 340 m/s. This is the reason that you’ll always see a lightning flash

before you hear the thunder that it produces. By counting the number of

seconds that it takes to hear the thunder after you see the lightning, you can

calculate how far away the lightning was. So here we go… LIGHTNING

FLASH 1, 2, 3, 4, 5 THUNDER. There it is!

Since distance = speed x time, the distance in this case is 340 m/s x 5 seconds which equals 1700 m or 1.7 km.

Light takes only a few millionths of a second to travel this distance. Another way of thinking about it is that every 3

seconds of delay represents 1 km.

Part C: Converting between m/s and km/hr

Converting between m/s and km/hr is actually fairly easy. You simply multiply the speed in m/s by 3.6. To convert

km/hr into m/s you divide by 3.6.

Let’s convert 10m/s into km/hr step by step to see where this 3.6 comes

from. 10 m is 10 thousandths of a km, so 10m/s = 10/1000s of a km/s.

But, one second = 1/3600 of an hour, so 10 m/s is the same as 10/1000 of

a km per 1/3600 (of an) hr.

It seems to be getting more and more and more complicated, but Maths is

like that sometimes. Let’s now simplify the expression. A fraction is

really the same as a division, so I can write it like this. As you may

already know, dividing by a fraction is the same as multiplying by the reciprocal of the fraction, so we can now get

this. I can then rearrange the order of the fractions to get this. (10 x 3600/1000)

3600/1000 = 3.6 which is our conversion factor. 10 m/s = 36 km/hr

So to convert m/s to km/hr you multiply by 3.6, and of course to convert the other way, from km/hr to m/s, you

divide by 3.6. A world-class 100 m sprinter, who can run the 100 m in 10 s, can run at an average speed of 10 m/s

which, as I said, is 36 km/hr.

A car travelling at 60 km/hr is travelling at 16.7 m/s. So in one

second it travels this far. (16.7 metres). Cars travelling at 100km/hr

travel at 27.8m/s. That’s a huge distance. We often don’t realize

just how far we travel every second when we’re in a car.

In an emergency, we actually travel quite a long distance just in the

time that it takes us to realize that there is an emergency, let alone

the distance we travel after we actually do something.

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This online reaction-time test accurately measures the time it takes you to click the mouse button when the light

changes from red to green. In this trial, I took an average of 0.26 seconds to respond each time.

Online Reaction-Time tester: http://getyourwebsitehere.com/jswb/rttest01.html

In 0.26 seconds, a car travelling at 60 km/hr, or 16.7 m/s, travels 16.7 m/s x

0.26 seconds which equals 4.3 m. In an emergency, say someone suddenly

steps out onto the road, 4.3 m is the just the distance I would travel during my

reaction time, before I even do anything. Then, a decision has to be made and

carried out. By the time you decide to, and then actually, either brake, swerve,

or, beep the horn, you’ve travelled even more distance.

Many crashes are caused by Driver 1 who suddenly pulls out in front of Driver 2,

who just doesn’t have enough time or distance to avoid a collision. However misses

are far more common than hits, of course. To increase your chance of a miss, never

speed, never get distracted by say your phone, and of course never drink too much

alcohol, because alcohol greatly increases the time it takes you to react to a dangerous

situation. And of course make sure that you’re not the driver who causes the crash.

Part D: Measuring Speed.

Since speed = distance over time, to measure speed, you need to measure the distance an

object covers and the time that it takes to cover the distance. To measure distance, you

can use, for example, a tape measure, or a trundle wheel. This trundle wheel measures

out 1 metre every time it turns.

To measure time, you need an accurate clock of some sort. The time of 15 seconds that was recorded for my 100 m

sprint was made with a hand-held stop watch. As we’ve seen though, human reaction time isn’t all that quick, so

any times that are recorded with stop watches are never going to be perfect. You might start too late or too early or

finish too late or too early.

But, even if the time was out by let’s just say 0.3 seconds, out of 15 seconds, this represents only a 2% error, so

stopwatches are okay when an event takes a fairly long time. (% error = 0.3/15 x 100% = 2%)

However stop watches aren’t all that useful when an event is really quick. For example,

it’s very difficult to measure the time that this soccer ball takes to travel 10 m. We need

a more accurate timer. In fact we can use a camera as a clock.

Video is really a series of still photos played one after the other in quick succession.

Each photo is called a frame. Different cameras record video at different frame rates, but 24, 25 and 30 frames per

second are the three most common frame rates. In this video recorded at 25 frames per second, each frame was

recorded 1/25 (or 0.04) of a second apart.

Various programs like QuickTime Player for example allow you to scroll through a video frame by frame by

pressing the arrow keys. We can count the number of frames to work out the time and we can then calculate the

speed.

So labelling the last frame that the ball was

stationary as “frame 0” and then counting the first

frame where the ball actually moved as frame 1, the

ball took 1 2 3 4 5 6 7 8 9 10 11 12 13 14 frames to

hit the wall. Since the video was shot at 25 frames

per second, 14 frames is a time of 14/25 of a second

or 0.56 s. The average speed of the ball was

therefore, vave = d/t which = 10 m/ 0.56 s which

equals 18 m/s or 64 km/hr.

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Professional soccer players typically kick a ball at twice this speed, and shots on goal occasionally reach three

times this speed. It’s interesting to note that once the ball and my foot are no longer in contact, the ball travels more

or less at the same speed.

Now my running, cycling and kicking abilities are completely irrelevant of course, but analysing speed

is very important in, for example, the design of vehicles and in the study of human motion.

Motion-capture technology uses a series of cameras which record the position of

reflective markers placed onto a subject. A computer then puts the information together

and builds up a 3D representation of the movement. A skeleton and muscles can also be

overlaid. The speed of each body part and the speed of rotation of each joint can be

calculated, and a very good estimate of the forces involved in the movement can also be

made. This can help athletes improve their technique.

Digital effects companies like Weta Digital use similar technology to create

brilliant, life-like animation effects for movies.

Now you can tell the speed of your car by looking at your speedometer, or

speedo.

It works a little like this bike speedo. There’s a

little sensor here that is triggered every time this magnet sweeps past it, and it sends

a signal up to the microprocessor here. The microprocessor measures the time

between each pass of the magnet, or in other words the time it takes for the wheel

to spin once.

The distance that the wheel travels every rotation has to be programmed into the unit.

These wheels have a diameter of 66 cm so they move a distance of

2.07 metres during every rotation. The microprocessor divides this

distance by the time taken and updates the speed of the bike after

every rotation of the wheel.

So, for example, if the wheel takes exactly 0.3 seconds to make one

complete rotation as it rolls along, then the speed of the bike has to

be the distance travelled, 2.07 m, divided by the time taken, 0.3

seconds, which equals 6.9 m/s (25 km/hr).

In a typical car speedo, a sensor is triggered every time the teeth of a toothed wheel that is attached to the wheels

passes a sensor, so the speed is updated more frequently.

Velocity is a really important concept. However, as we’ve already seen, things are always changing their velocity.

When something does change its velocity it is said to have accelerated, and it’s acceleration that we’re going to

look at in our next episode. See you then.

Credits:

ATHLETICS Men's 100M Final - 28th Summer Universiade 2015 Gwangju (KOR) by FISUTV.

License: Creative Commons.

Sydney Opera House - Dec 2008.jpg

(https://commons.wikimedia.org/wiki/File:Sydney_Opera_House_-_Dec_2008.jpg) by DAVID

ILIFF. License: CC-BY-SA 3.0

Milos Raonic slice serve to Novak Djokovic slomo BNP Indian Wells by Jim Fawcette. License:

CC-BY-SA 3.0

The Online Reaction Time Test, © 2002 by Jim Allen, gywh.com. Used with permission.

Shedding Light on Motion Episode 1: Speed www.liacoseducationalmedia.com Page 8 of 8

Footage and photos of NASA’s Mars Climate Orbiter by NASA.

Dashcam footage courtesy of Dash Cam Owners Australia.

Motion-Capture Footage courtesy of Dr James Shippen (see mendip89), Centre for Mobility and

Transport, Coventry University, UK.

Crash-Test footage © ANCAP Safety Ratings. Used with permission.

Usain Bolt photo by Erik van Leeuwen

https://commons.wikimedia.org/wiki/File:Usain_Bolt_smiling_Berlin_2009.JPG is licensed under the

GNU Free Documentation License.

Vision from the special effects created by Weta Digital and used in

the making of Dawn of the Planet of the Apes © 20th Century Fox.

Used in what we consider “Fair Use” for the purposes of critical

review and education.