Linear Motion Earth spins on axis at 700 mph Are you moving? How do you know? Earth spins on axis at 700 mph Earth revolves around sun 72,000 mph Solar system moves thru galaxy 675,000 mph So I ask again, Are you moving?? Best answer is another question: Relative to what? To what frame of reference are we judging motion? Since all motion is really measured relative to a particular “background”. The typical frame of reference we assume, if none is stated, is that of the Earth, so with that, who’s are you moving?

Speed Measures how fast something moves or the rate at which distance is covered Rate is any quantity that involves dividing by time Ex… eq’n: v = Δd/Δt called the constant speed eq’n where Δ is the Greek letter “delta” – it means “change in” v is for speed (and eventually velocity) Δd is the distance or displacement also thought of as the change in position Δt is the time interval passed units: any distance unit / any time unit Ex:

Explaining Table 2.1 on pg 12: x m/s ≈ 2x mph ≈ 4x km/h This is for estimation purposes – it does not give an exact conversion, but that’s OK, that’s all you’ll ever need to do in this class! Really what you’ll need to do most often is turn a “new” unit of speed into the one you know (mph), so x m/s x 2 ≈ ____ mph and x km/h ÷ 2 ≈ ____ mph Try some: 10 m/s ≈ 110 km/hr ≈ 346 m/s ≈ 43.7 km/h ≈ 178.62 m/s ≈

2 Types of Speed Instantaneous – at a given instant - Read from a speedometer or radar gun We’ll be getting equations to find it soon Average – over any time longer than an instant doesn’t provide info on mins or maxs eq’n: vavg = total distance / total time Why not add up individual speeds and divide by how many there are? If you spend different amounts of time at each speed, it won’t work out.

Velocity Provides information about both speed & direction Ex: 60 mph vs 60 mph, North (Doesn’t seem like a big difference, but it can be and we’ll be seeing examples of that later…) 2 Types of Velocity Constant – the object maintains the same speed in the same direction (straight line) Changing – the object changes either speed OR direction So which for a horse on a Merry-Go Round? changing due to circular path - direction What 3 means does a car have to change v? brake, gas and steering wheel

Acceleration Is the rate at which velocity CHANGES – so you’re either speeding up slowing down OR turning to accelerate, If not doing one of these, then a = 0! It does not measure how fast you’re going, it measures how fast you’re changing how fast you’re going! It does not mean “to be moving fast” You could have a high v , but a low or 0 a: Ex: You could have a low or even 0 v, but a high a:

Better eq’n for math problems: a = vf – vi Eq’n: a = Δv / Δt, but don’t use this form when solving math problems!! Better eq’n for math problems: a = vf – vi Δt where vf is final velocity and vi is initial velocity This eq’n reinforces that there must be 2 different velocities for an object to accelerate Often one of them will = 0, but must state that as part of the given and insert it into the original eq’n Units: Any speed units / any time units Examples * mph / s as in “this Audi R8 does 0 to 60 in 4.6 seconds” * or km/h / s if you live in any other country…

What might need units of m/s / hr for its acceleration? Something that accelerates very slowly! Standard acceleration unit in physics: m/s / s (or m/s2) But for final math answers, you must write this as: “Gains/loses (#) m/s every second” Let’s do some examples: A toy truck goes 3 m/s in the 1st second 5 m/s in the 2nd second 7 m/s in the 3rd second What’s its acceleration? a = gaining 2 m/s every sec A plane landing goes 50 m/s in the 1st sec 40 m/s in the 2nd sec 30 m/s in the 3rd sec a = losing 10 m/s every sec

Let’s try a few examples… Ex #1. A car took off from a red light and reached 27m/s in 5.8 s. What was its acceleration? gains 4.65 m/s every s

Ex #2. A jet plane, moving at 253 m/s, runs into a storm which causes it to slow to 175 m/s in 38 s. What was its acceleration? loses 2.05 m/s every s

Ex #3. A robot’s specifications says it can accelerate at 1. 5 m/s2 Ex #3. A robot’s specifications says it can accelerate at 1.5 m/s2. If its “forward” button is held on for 17 s, how fast should it be going? 25.5 m/s