What is 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 – called the frame of reference. The typical frame of reference we assume, if none is stated, is that of the Earth, so with that, 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 = Δx/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) Δx is the distance or length of path traveled Δt is the time interval passed units: any distance unit / any time unit Ex: All scalars so no vector symbols needed on variables.

Useful Estimation Conversion 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 when going from metric into our system! Really what you’ll need to do most often is turn a “new” unit of speed into the one you know (mph): ___ m/s x 2 ≈ ____ mph and ___ km/h ÷ 2 ≈ ____ mph Try some: 10 m/s ≈ 110 km/hr ≈ 346 m/s ≈ 43.7 km/h ≈ 178.62 m/s ≈

Types of Speed Constant – keeps the same speed for entire trip Changing Instantaneous – at a given instant - read from a speedometer or radar gun Average – over any time longer than an instant doesn’t provide info on mins or maxs eq’n: v = total distance / total time If you used this for a long trip, you’d need to include the time spent stopped for gas or food, etc… so not very useful.

Speed vs Velocity If speed is the rate at which distance (Δx) is covered, velocity is rate at which displacement (Δx) is covered. Recall, distance is the length of the path taken, while displacement is the length from start to finish, and Δx is displacement or change in position, xf – xi Since displacement is a vector, so is velocity. Similar variables & eq’ns: Speed: v = Δx / Δt Velocity: v = Δx / Δt And both use the same units: m/s Doesn’t seem like there’s much difference, but there can be… What’s the speed of someone who runs 8 laps around a ¼ mile track in 30 min? What the velocity of that person?

Types of Velocity Constant – keeps the same speed in a straight line Ex: Changing – the object changes speed OR direction So which for a horse on a Merry-Go Round? changing direction due to circular path What 3 means does a car have to change v? brake, gas and steering wheel Instantaneous – at a given instant lots of equations coming to help us find this Average – over any time longer than an instant doesn’t provide info on mins or maxs the eq’n v = Δx/Δt called the average velocity eq’n

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:

Eq’n: a = Δv / Δt, but don’t use to solve math problems!! 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

The Constant Acceleration Equations missing variable? Δx vf vi Δt a vf = vi + aΔt Δx = vi Δt + ½ a Δt2 Δx = vf Δt - ½ a Δt2 vf2 = vi2 + 2a Δx Δx = (vi + vf) Δt 2 To use these equations, you will be given a problem that contains 3 given pieces of information and 1 unknown so that 1 of the 5 variables is completely left out: choose the equation that is missing that ignored variable. Try some…

Let’s try a few examples… Ex #1. A car took off from a red light and reached 27 m/s in 5.8 s. What was its acceleration? gains 4.65 m/s every s Who got 27 m/s2???

Ex 2. A car, starting at 28 m/s, accelerates at a constant rate so that in 5.3 s, it was going 52 m/s. How far did the car travel in this time? 212 m

Ex 3. A motorcycle ends up traveling at 47 m/s after having undergone a constant 1.7 m/s2 acceleration over 184 m. What was its starting speed? 39.8 m/s

Ex #4. 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 but who got + 168??? Bring your own calc to class!

Ex #5. A robot’s specifications says it can accelerate at 1. 5 m/s2 Ex #5. 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

Ex #6. If a drone flying at 7. 9 m/s slows to 1 Ex #6. If a drone flying at 7.9 m/s slows to 1.6 m/s over a distance of 11.2 m, what’s it’s acceleration? loses 5.34 m/s every sec