Distance, Time & Speed

A long time ago in a land far, far away… What is “distance”? What is “distance”? Distance – the amount of space between two points. Distance – the amount of space between two points. We measure distance using kilometres (km), metres (m), centimetres (cm) or millimetres (mm) – it depends on how big the space is to be measured. We measure distance using kilometres (km), metres (m), centimetres (cm) or millimetres (mm) – it depends on how big the space is to be measured. Now for the tough one…What is “time”? Now for the tough one…What is “time”? Time – The duration between events. (Easy stuff!) Time – The duration between events. (Easy stuff!) We measure time using days (d), hours (h), minutes (min) or seconds (s) – depending on how long we have to wait. We measure time using days (d), hours (h), minutes (min) or seconds (s) – depending on how long we have to wait.

Converting Units In order to solve problems we must be able to convert units of both distance and time – it’s easy stuff though…just watch. In order to solve problems we must be able to convert units of both distance and time – it’s easy stuff though…just watch. Let’s do distance first… Let’s do distance first…DISTANCE x1000 x100 x10 x1000 x100 x10 kmmcmmm ÷1000 ÷100 ÷10 ÷1000 ÷100 ÷10

Converting Time TIME x24 x60 x60 x24 x60 x60 dhmin s ÷24 ÷60 ÷60 ÷24 ÷60 ÷60

Think, Ricky…Think! Our old friend Julian, from the Sunnyvale Trailer Park, says this to Ricky whenever he misses the obvious and comes up with something that is totally wrong. Our old friend Julian, from the Sunnyvale Trailer Park, says this to Ricky whenever he misses the obvious and comes up with something that is totally wrong. You might be a “Ricky” if you don’t watch it…you have to remember when to divide and when to multiply…it makes a huge difference. You might be a “Ricky” if you don’t watch it…you have to remember when to divide and when to multiply…it makes a huge difference. Lets see what I mean… Lets see what I mean… How many metres are in 2.5km? How many metres are in 2.5km? Well…I know that one km has 1000m…So do I divide or multiply by 1000? Well…I know that one km has 1000m…So do I divide or multiply by 1000? If I divide (2.5 ÷ 1000) I get m. (Less than a single metre…is 2.5km less than a single metre?) If I divide (2.5 ÷ 1000) I get m. (Less than a single metre…is 2.5km less than a single metre?) If I multiply (2.5 x 1000) I get 2500m. If I multiply (2.5 x 1000) I get 2500m. Which one seems right?…Think, Ricky…Think! Which one seems right?…Think, Ricky…Think!

Boys, I know what I’m doin’! Make sure you have the number written correctly. Make sure to use the right conversion factor. Multiply or Divide the two numbers. Make sure your answer makes sense – think Ricky! Pass Grade 10!!!

Practice Problems in Converting Try these practice problems. Convert the following units… Try these practice problems. Convert the following units… a) 250m = kmk) 360s =min b) 1475cm =ml) 45min =h c) 3.45km =mm) 3.5h =min d) 459mm =cmn) 75min =s e) 20cm =mo) 3.75d =h f) cm =kmp) 5d =min g) 7.56km =mmq) 2400min =d h) 8340mm =mr) 3600s =h i) 96.45m =mms) 58000s =d j) 2470km =cmt) 0.68d =s

Converting Units These are the answers to the practice problems. These are the answers to the practice problems. a) 250m = 0.25kmk) 360s =6min b) 1475cm = ml) 45min =0.75h c) 3.45km = 3450mm) 3.5h =210min d) 459mm = 45.9cmn) 75min =4500s e) 20cm = 0.2mo) 3.75d =90h f) cm = 5.06 kmp) 5d =7200min g) 7.56km = mmq) 2400min =1.67d h) 8340mm = 8.34mr) 3600s =1h i) 96.45m = 96450mms) 58000s =0.67d j) 2470km = cmt) 0.68d =58752s

Speed Speed is a measure of the amount of distance traveled per unit of time. We say the speed of a car is 100km/h – it travels 100km in 1 hour. Speed is a measure of the amount of distance traveled per unit of time. We say the speed of a car is 100km/h – it travels 100km in 1 hour. The units we use to measure speed also tell us how it is measured/calculated. The 100km/h shows us that distance (km) is divided by the time (h). The “/” in the unit is the same as a division sign. The units we use to measure speed also tell us how it is measured/calculated. The 100km/h shows us that distance (km) is divided by the time (h). The “/” in the unit is the same as a division sign. So to calculate speed, we simply take the distance and divide it by the time. So to calculate speed, we simply take the distance and divide it by the time.

The Speed Formula The formula for speed is shown below… The formula for speed is shown below… v = Δd Δt Δt In this formula: In this formula: “v” is the symbol for speed. “v” is the symbol for speed. “Δ” is the Greek symbol Delta = change. “Δ” is the Greek symbol Delta = change. “Δd” is the symbol for “change in distance”. It can be measured as Δd = d 2 – d 1. (Change = Final – Initial) “Δd” is the symbol for “change in distance”. It can be measured as Δd = d 2 – d 1. (Change = Final – Initial) “Δt” is the symbol for “change in time”. It can be measured as Δt = t 2 – t 1. (Change = Final – Initial) “Δt” is the symbol for “change in time”. It can be measured as Δt = t 2 – t 1. (Change = Final – Initial)

The Speed Triangle You may also use a formula triangle – see below: You may also use a formula triangle – see below: This triangle gives you the formula for any one of the three parts of the speed equation. You can now solve for speed, distance or time. (Cover it up and see what’s left) This triangle gives you the formula for any one of the three parts of the speed equation. You can now solve for speed, distance or time. (Cover it up and see what’s left)

Types of Speed Average Speed – The total distance traveled divided by the total time elapsed. Average Speed – The total distance traveled divided by the total time elapsed. Instantaneous Speed – The speed an object is traveling at a particular instant in time. Instantaneous Speed – The speed an object is traveling at a particular instant in time. Constant Speed – Traveling the same distance for each successive unit of time. Constant speed is also known as uniform motion. Constant Speed – Traveling the same distance for each successive unit of time. Constant speed is also known as uniform motion.

How to Solve Motion Problems For every problem, you must show: For every problem, you must show: – The correct formula. – Proper substitution of values & units. – The correct answer with proper units. Every time one of these things is missing – you will lose a mark – I promise. Every time one of these things is missing – you will lose a mark – I promise. Sample Problems (We will do together.) Page 355 – Sample Problem #1 Page 355 – Sample Problem #1 Page 356 – Sample Problems #2 & #3. Page 356 – Sample Problems #2 & #3. Page 357 – Sample Problem #4 Page 357 – Sample Problem #4

Just a Few Reminders… Always check your measurements and conversions!!! Always make sure your answers make sense…or else!!! Listen to your teachers, stay out of trouble and it’ll be mission accomplished!!!

THE END!!!