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Physics – Motion
Why do we care about motion?
Motion is the study of how objects move without regard to the forces that make them move.
It is one of the first units you would study if you took Physics in grade 11, community college or university The concepts you will learn allow you to figure out your average speed on a trip and the time it would take to make a journey
The concepts are expanded on in further years and could be used to determine where a rocket will land, how long it would take for a space probe to get to Mars or how fast a car was going before it was in an accident if you know the length of the skid marks What careers would use this?
Physicist (obviously) Engineer (engineers use physics, chemistry, math and sometimes biology to design buildings, machines, devices, etc so that they are safe and don't waste material) Police officers with their radar guns or if they do accident reconstruction Nascar Drag Racing Pilots, Airports Trucking dispatchers for planning shipments Everyday people when they are planning trips
Displacement vs. Distance
Quite often these two terms are used as if they are the same thing. In reality they are the same for some situations but not for others. Let's look at what they are and why they are sometimes are the same and sometimes they are different.
Displacement - how far a person or object is from where they started in a straight line
- have you ever heard the term "as the crow flies"? This old saying means that a crow would fly directly from one point to another in a straight line
- it also includes direction. Which could be left, right, up, down, east, west, or an angle depending on the question
Distance - how far a person or object travels in total regardless of the number of turns
- does not have a direction
The best way to visualize this is with examples.
Let's look at the example of a river. Rivers rarely run in a totally straight line for very long.
If you wanted to paddle from Point A to Point B you would travel the total distance of the river.
How far you travel is the distance. The crow could fly directly from Point A to B in a straight line. This is the displacement from Point A to Point B
Measurement
Now that we have talked a bit about displacement and distance let's move on.
What are some of the units we can measure displacement or distance with?
What are some of the tools we use to measure displacement or distance?
Activity 1: Displacement vs. Distance
Calculating Displacement
Now that we have discussed how to find distance and displacement by measuring how do you find the displacement if you are given points? In order to find the displacement you need to have the starting and end points
d = x - xo d = displacement x = final position xo = initial position
Example M.2 Brendan walked from Walmart to his home. If home was 300 away, what is the a)Distance? b)Displacement?
Example M.3 Nathan was at his friend's house which is 2km west of town. He lives 4km east of town. a) Calculate his displacement from his friend's house when a) he stops in town b) when he gets home. c) calculate the distance travelled.
Example M.4 Stella is walking on the park trails. She starts at the 14km marker. She walks west and takes a break at the 5km marker. a) What is her displacement b) What is her distance?
Example M.5 Jessica lives in a small town 35km east of Kansas City. She goes on a trip that gives her a displacement of -250km. Where does she end up relative to Kansas City?
Speed or Velocity?
Both measure how fast an object is going.
Speed - is a measurement of the distance an object has travelled divided by the time it was travelling, without regard for direction.
So how do you calculate velocity and speed? Well, generally in physics we are concerned with velocity because often direction is important and as we said distance doesn't include direction. We will go into more detail later about this.
Velocity is defined as displacement divided by time. So it would look like this: v = d t
The problem with this is that we are going to need to expand on this equation later so we need to write it in a different form so that it works with other equations later.
So v = x - x 0 we replaced d with x-xo t
then vt = x - xo we multiplied both sides by t
x 0 + vt = x add xo to both sides
finally x = xo + vt -switch sides, because all equations start with one variable -also, because we will be using different types of velocities we need to be specific. We us the to signify that this average velocity.
x = xo + vt x = final position xo = initial position v = average velocity t = time interval
**Note : v is used as average velocity but can also be used as constant velocity if the object stays at a constant rate such as a car on cruise control.
Example M.7 Aaron sets out from his house for a bike ride. He slows down and speeds up along the way as you would expect on a bicycle but averages a velocity 8m/s east for the trip. If he bikes for 1800 seconds where does he end up. Note: if no initial position is stated you can assume it is zero (0).
Example M.8 Sally usually rides her bicycle to school on sunny days. She lives 2000m to the east of school. On a good day without a lot of traffic she can get to school in about 700 seconds. Determine her average velocity.
Example M.9 Henry and Francis are having a race. Henry is a bit slower but gets a head start. Francis will start at 0m and he gives Henry a 20m head start. They will both race to the 100m finish line. If Henry can run an average of 4m/s and Francis can average 6m/s determine how long it takes a) Henry to get to the finish line b) how long it will take Francis to get to the finish line. c) How much of a head start should Henry get if they are to arrive at the same time?
Example : Follow the example below to convert 0.5km to m.
Step 1 : make a table or chart like the one below
Step 2 : Put the value you are starting with in the top left corner
Step 3: In this method of converting we multiply all values on the top together and divide by all the values on the bottom. This includes all the numerical values and the units. By doing this we will end up with the same units on the top and bottom and be able to eliminate the units we started with.
In this example since we have km on the top to start we need to put km on the bottom in the next set of spaces to eliminate the km.
Step 4 : Since we want to convert to m it will go on the top. We need to look in the table to see what the relationship is between km and m. In our table the relationship is 1km=1000m. We can also write this as a ratio of 1km/1000m or 1000m/1km. (Some tables may have them reversed as 1m=0.001km.)
The ratio then goes in our table with the same numerical value assigned to each unit as we found them in the table.
Note that in the table the ratio is still the same as it was in the table. We just need to figure out where to put the units we want to get rid of and then put the numbers in as stated in the table. It isn't always a 1 on the top or bottom, that is decided by the units.
Step 5: Do the math and solve for the answer. (Remember we multiply the top and divide by the bottom.)
So 0.5km equals 500m. Which makes sense since 1km = 1000m
Name Prefix Unit Equivalent amount of base unit
kilometer 1km 1000m
hectometer 1hm 100m
dekameter 1dam 10m
meter 1m 1m
decimeter 1dm 0.1m
centimeter 1cm 0.01m
millimeter 1mm 0.001m
micrometer or micron 1μm^ 0.000001m
1 day 24 hours
1 hour 3600 seconds
1 min 60 seconds
Let's convert 36km/h to m/s
Before we practice let's do one more Let's convert 20 m/s to km/h
Example M.11 Convert the following a) 25 m/s to km/h
b) 108 km/h to m/s c) 2400 cm/min to m/s
Changing velocities
So far we have talked about average velocity. Remember that we can use the same equation if it is constant velocity.
However, in Physics we are often interested in knowing the velocity at the beginning of a time interval and at the end of the time interval. We will use these values at a later point to calculate acceleration but right now we are going to use them to calculate average velocity and it turn displacement.
First thing we need to discuss is the variables. We will use the following:
vo - this is pronounced V not. It is used to signify the initial velocity in a situation. It can be measured in the regular units for velocity (km/h, m/s or other less common versions)
- think of the subscript 0 (little 0) as representing the beginning when time is starting or equal to 0!
v - this is simply v and signifies the final velocity.
How do you know which is which. This is where the importance of English comes in. Usually the initial velocity is in past tense and the final is in present of future tense. See the scenarios below for examples
vo (initial velocity) v (final velocity) was travelling at... ended up travelling...
initally... finally. is moving at... speeds up/ slows down to... at rest... accelerates to...
was moving at.... comes to complete stop.
When trying to figure out problems in Physics or anything for that matter read the question and use your knowledge about English and Math to break it into parts and then choose a direction or equation.
Example M.14 : Patrick and Jeremy are driving in Sussex at 54 km/h towards Apohaqui. Once they reach the highway they speed up to a velocity of 110 km/h. a) What is their average velocity? b) What was their displacement within this time period if it took 8 seconds to reach 108km/h?
Example M.15 Kurt is travelling down the highway when he has to come to a complete stop for highway construction. His average velocity while slowing down was 54km/h north. How fast was he travelling initially?
Example M.16: Lucy is travelling north on the highway when she notices a large plume of smoke over the next hill. At the moment she sees the smoke she also notices she is next to the 167km marker on the side of the road. Being a defensive driver she decides to slow down. She comes to a stop at the 168km marker. It took her 1 minute to get between the 2 markers. How fast was she going at the moment she started to slow down. This one is a bit tricky. Break it into parts.
Acceleration
Acceleration is the change in velocity over a specific time interval. As you will remember velocity has a measurement and a direction. Generally when we talk of acceleration we are talking of a change in measurement/magnitude but in some instances we would have a constant rate but a change in direction. We won't be doing those type of question this semester though.
You will also see acceleration defined as the rate of change of velocity. The term rate means how fast something is changing over time. In the concept of acceleration this means how fast the velocity is changing.
Let's consider two scenarios. In each scenario the object is initially at rest and accelerates to 20m/s. In the first scenario this process takes 5 seconds and in the second it takes 10 seconds. Using your experience you would say that the velocity increased at a greater rate in the first scenario in order to achieve the final speed in less time.
If we were to write this in terms of variables it would look like:
a = Δv t
Rearranged it is expressed in its most common form below
v = vo + at v = final velocity (m/s) vo = initial velocity (m/s) t = time (seconds) a = acceleration (m/s^2 )***
going 250km/h. If the parachute provides about -12m/s^2 of acceleration determine how long it would take to reduce his velocity to 100km/h.
Acceleration situations without final velocity
Sometimes we want to determine the displacement of an object and we don't know the final velocity. In all the situations so far we have either had the average velocity or we had the initial and final velocity and could determine the displacement. We can still do that but long ago Physicists determined a formula that is a combination of the previous formulas. We will also look at this equation again when we look at graphing.
x = xo + vot + ½at^2 x = final position (m) xo = initial position (m) vo = initial velocity (m/s) a = acceleration (m/s^2 ) t = time (s)
Example M.21 Danielle is moving at 1.5m/s east when she accelerates at 0.5m/s^2 east for 8 seconds. a) How far did she travel during this time? b) How fast was she travelling at the end of this period?
Example M.22 Chris is running a 50m race. If he starts from rest and it take him 8 seconds determine his average acceleration. Assume he is heading north.
Example M.23 Martha is travelling east when she puts her brakes on. Her acceleration is -4.2m/s^2. If she slows for 5 seconds and travels 0.20km east how fast was she going initially?
Acceleration Due to Gravity
In all examples up to this point we have dealt with objects moving on the ground. We need to look at objects that are thrown in the air or are falling. Objects that are falling or going up in the air without a power source (like rockets or planes) have an acceleration that is created by the pull of the Earth's gravity. This acceleration is assumed to be constant near the Earth's surface and is equal to -9.8m/s^2.
a = g = -9.8m/s^2 *a is also called g because it is due to gravity
Example M.24 A kangaroo can jump quite high due to its strong legs. A kangaroo is observed and determined to jump to a maximum height of 2.5m. If it is in the air for 0.70s and experiences an acceleration of -9.8m/s^2 determine the initial velocity of the kangaroo.
Example M.25 A group of grade 10 students are trying to test this acceleration of gravity concept. They go on the roof of their school (they don't have a balcony so don't ask if we can go on the roof) and do repeated tests. They find an average time to hit the ground of 1.23 seconds. If gravity is equal to what they assumed, how tall is the roof of the school?
