Chapter 2 Linear Motion

2.1 Motion Is Relative When we describe something in motion, we are comparing it to something else. For example: A car is driving 45 miles per hour: You only know it is moving because the road and trees around it are staying still.

2.1 Is it possible for an object that appears to be at rest, move? Yes, even as we stand still we are hurtling through space.

2.1 We usually describe motion relative to the Earth’s surface.

2.1 This means when we describe motion we do it relative to something: The train is leaving the station or is the station leaving the train? A car in the Indy 500 travels 500 miles in the race but ends up at the same point. On the school bus traveling at 30 mph you throw a ball to a classmate, how fast is the ball moving?

2.2 Speed Speed is a “scalar quantity” – this means it does not include direction. Ex: I am running at 10mph, but I don’t tell you where – this is speed. Speed is the distance covered divided by the time it takes. (mi/h; m/s; km/hr) Lightning BoltLightning Bolt Unbelieveable Is that possible?UnbelieveableIs that possible?

2.2 Speed Speed is a measure of how fast something is moving. We think of it in two ways: Instantaneous speed Average speed Speed racers

2.2 Instantaneous Speed – speed at a particular moment You are in a car heading downtown, and you can see from the speedometer your speed is 40 mi/h (or mph). Downtown is 10 miles away at this speed. How long would it take you? Is this true?

2.2 Average Speed It would take us a lot longer than 15 minutes to drive downtown because of the traffic where we have to slow, stop, start, accelerate, slow, stop, etc., etc,. Therefore in planning a trip we think about average speed Avg. speed = TOTAL distance covered/time S = d/t

2.2 Average Speed If downtown is 10 miles and it will take me 30 minutes then my average speed is 20 mi/h. This is a lot different from my Instantaneous Speed of 40 mi/h. If we know our average speed and the time traveled we can arrange the formula to tell us our distance traveled. Total distance = avg. speed X time

What is the speed of a man running 8 miles in 2 hours? Answer: s = d/t 8 miles (total distance) / 2 hours (time interval) s = 8/2 = 4 miles/hour

If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 sec? In 1 min? S = d/t 25 m/s = d/10 sec D = 25m/s * 10 sec D = 250 meters 1 min = 60 sec S = d/t 25 m/s = d/60 sec D = 25 m/s * 60 sec D = 1500 m

Remember: “per’ means “every” So, 45 miles per hour is saying that something moves a distance of 45 miles EVERY hour (distance/time)

2.3 Velocity Velocity is a “vector quantity”–this means is has Speed and Direction. If a car travels at 60 km/h we have defined its speed, but if we say it is traveling at 60 km/h heading north we have defined its Velocity!

2.3 Going in a straight line at the same speed is called Constant Velocity. But if we change our speed (brake at a light) and/or our direction (turn a corner) then we have a Changing Velocity. If we change our speed by going faster –we call this Acceleration

2.3 Velocity Velocity is speed with direction. Constant velocity is remaining the same or CONSTANT speed AND direction. Changing velocity is NOT remaining the same speed AND/OR direction.

2.4 Acceleration Acceleration is changing velocity; either speeding up or slowing down. Amazing!!!Amazing!!! ACCELERATION IS NOT VELOCITY change of velocity Acceleration = time interval

2.4 Acceleration is the rate at which velocity changes with time.

2.4 When we accelerate in a car from stop to 60km/h in 5 seconds. We have changed our speed and this is Acceleration. The same applies when we are in a car that slows –this is called negative acceleration or Deceleration.

2.4 Acceleration also applies to changes in direction. We feel the effects when in a car we are pushed to the side when we turn a sharp corner. Blue AngelsBlue Angels If a = Δv/Δt, then this is measured in units km/hr/s or more commonly m/s 2

A plane travels from 0 mps to 60 mps in 6 seconds. What is its acceleration? Answer: Change in velocity= ending velocity - beginning velocity Change in velocity = 60 m/s – 0 m/s = 60 m/s 60 m/s (change in velocity) / 6 second (time interval) 60 m/s / 6sec = 10 m/second/second OR 10 m/second 2

2.5 Free Fall: How Fast Why does an object fall to the ground when dropped? GRAVITY Gravity pulls objects towards the Earth at an acceleration rate of 10 meters/sec/sec.

2.5 If a rock is dropped off the side of a cliff we would expect it to fall and during the fall we would expect it to accelerate. If there was no air resistance its speed would increase by approximately 10m/s every second. So after 5 seconds its speed would be 50m/s

2.5 If the rock was thrown up into the air we would still see the rate of velocity change as 10m/s 2. But for the first few seconds it would be decelerating, then stopped for a fraction of a second, before it started its acceleration toward the ground

2.5 If we are on a cliff on the Moon, therefore there is no atmosphere –a vacuum and we dropped a feather and the rock at the same time, they would fall together with the same acceleration. Of course when on earth where we have air things change because of air resistance. Would you rather jump out of a plane with a parachute or not and why?

2.5 W/O Air ResistanceW/Air Resistance

2.5 Free Fall: How Fast Elapsed time – the time that has passed since the beginning of the fall. In free fall, an object accelerates at a rate of 10 m per second every second

2.5 Free Fall: How Fast To calculate velocity in free fall: velocity = acceleration X time or v=gt Remember: g= acceleration due to gravity

2.6 Free Fall: How Far How fast something falls is different from how far it has fallen

2.6 Free-Fall: How Far? To calculate distance fallen: distance=1/2g X time 2 or d=1/2gt 2

Elephant VS Feather With no other resistance, they both fall with the SAME ACCELERATION: 10 m/sec/sec

But we all know the elephant would land first. Why? Answer: AIR RESISTANCE Air resistance alters the motion of falling objects by adding additional forces.

2.7 Graphs of Motion Equations and tables are not the only way to describe relationships such as velocity and acceleration.

2.7 You can graph the relationships of both time and speed and time and distance by using x and y values.

Distance vs. Time

What is the slope on a distance vs. time graph = to? Slope = rise/run Slope = Δy/Δx Slope = distance/time Slope = speed

Velocity vs. Time (Constant)

Velocity vs. Time (Changing)

What is the slope on a distance vs. time graph = to? Slope = rise/run Slope = Δy/Δx Slope = velocity/time Slope = acceleration

Acceleration vs. Time Graph

Graphs of Motion

Chapter 2 Know the difference between speed, velocity and acceleration Know how to calculate the velocity and distance of an object in free fall Know what “g” is

Chapter 2 Terms: AccelerationRate Average speedRelative Elapsed timeSpeed Free fallVelocity Instantaneous Speed

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