Speed vs. Velocity

Speed vs. Velocity Velocity, v (meters/second with direction) • vector • rate of change of displacement • change in displacement per unit time Speed (also meters/second but NO DIRECTION) • scalar • Rate of change of distance • Change in distance per unit time

Speed vs. Velocity Velocity, v (meters/second) • vector • rate of change of displacement • change in displacement per unit time Speed (also meters/second) • scalar • Rate of change of distance • Change in distance per unit time Run around the 400m track in 4 min. What is your speed (m/min)? What is your velocity (m/min)?

Velocity and speed • Speed is scalar. Has no direction. • 8 m/s • Velocity is a vector. It does have direction. • 8 m/s North • 8 m/s at 53 degrees. • 8 m/s up

Equations • Speed Average Speed = distance traveled / time s = d / t • Velocity (for each axis) Average Velocity = displacement / time vx = Δx/Δt and vy = Δy/Δt • For those of you in calculus: • vx= dx/dt and vy=dy/dt

Question: • The Earth is 1.5 * 1011 meters from the sun. • A year is 3.2 * 107 seconds. • If the orbit is a perfect circle, what is the speed of the earth over six months? • What is the velocity?

Question: • The Earth is 1.5 * 1011 meters from the sun. • A year is 3.2 * 107 seconds. • If the orbit is a perfect circle, what is the speed of the earth over six months? • Distance / time • 4.7 * 1011 m / 1.6 * 107s = 3.0 * 104 m/s • What is the velocity? • Displacement / time • 3.0 * 1011 m / 1.6 * 107s = 1.9 * 104 m/s @ 180 deg

Question: • The Earth is 1.5 * 1011 meters from the sun. • A year is 3.2 * 107 seconds. • If the orbit is a perfect circle, what is the speed of the earth over one year? • What is the velocity?

Question: • The Earth is 1.5 * 1011 meters from the sun. • A year is 3.2 * 107 seconds. • If the orbit is a perfect circle, what is the speed of the earth over one year? • Distance / time • 9.4 * 1011 m / 3.2 * 107s = 3.0 * 104 m/s • What is the velocity? • Displacement / time • 0. Displacement was zero, so velocity is zero as well.

Problem • A girl scout travels 15 meters East at 1 m/s to drop off some cookies. It takes her 180 seconds to drop them off. She then travels 17 m North at the same speed to drop off a second box of cookies at a different house. • What was her displacement? • What was her average velocity during this time?

Distance • Displacement: DOES NOT CARE ABOUT PATH. START TO STOP!!! Use Pythagorean Theorem and SohCahToa to find the Angle. Vel = Disp / Time Time = 15 + 17 + 180 23 m @ 49 deg 17 m 15 m

Problem • A girl scout travels 15 meters East at 1 m/s to drop off some cookies. It takes her 180 seconds to drop them off. She then travels 17 m North at the same speed to drop off a second box of cookies at a different house. • What was her displacement? • What was her average velocity during this time? • Now she waits another 180 seconds and travels 7 m West at the same speed. • Displacement? • Velocity?

Acceleration • Acceleration “a” is the change in velocity per time. x vector ax = Δvx/Δt y vector ay = Δvy/Δt scalar a = Δs/Δt • 2 kinds of vector acceleration:

Acceleration • Acceleration “a” is the change in velocity per time. • 2 kinds of acceleration: • Changing Magnitude • OR Changing direction • If either the number OR direction changes, then acceleration has occurred. A force had to act.

Acceleration • Acceleration “a” is the change in velocity per time. • Acceleration is when motion is changed due to the action of a force. Will use this definition later. For now: Accel. is a change in magnitude or direction.

Acceleration • Question: • A track person runs around the football track at a constant speed of 100 m/min. Their speed does not change 1 little bit. Did they accelerate?

Acceleration • Question: • A car goes around a curve on the interstate at a constant 60 mi/h. Did they accelerate?

Acceleration • Slang: De-acceleration or Deceleration is NOT A WORD. • What’s deceleration mean? Negative Acceleration. • What does Negative Acceleration mean? Magnitude or number in velocity is decreasing.

Acceleration • What does Negative Acceleration mean? Magnitude or number in velocity is decreasing. • 30 mi/h to 10 mi/h is a -20 mi/h acceleration (neg accel). • -30mi/h to -10 mi/h is a +20 mi/h acceleration (pos accel).

4. Acceleration • When a body changes its velocity it is said to undergo positive or negative acceleration. • Rate at which the velocity is changing • human body reacts to acceleration not velocity • it is an accelerometer not a speedometer • If you know calculus: a = dv/dt or d2x/dt2 average

Acceleration • Units – since it’s velocity per time • Or

Acceleration • If an object starts at rest, and has an acceleration of 1 m/s2, what will the velocity be at each time in the table? • What if it starts at 5 m/s?

Acceleration • If an object starts at rest, and has an acceleration of 1 m/s^2, each second that elapses, the velocity increases by 1 m/s . • If it started at 5 m/s, it still gains 1 m/s for each second that elapses.

Acceleration Equation • a = Δv/ Δt • Δv = a*t • The same equation, written differently (Δv= vf – vi) • vf = vi + at

Acceleration • If an object has “negative acceleration” that means it is slowing down. • If a car is traveling at 20 m/s, and has an acceleration of -1 m/s^2, it will slow down by 1 m/s for each second that elapses. • After 20 seconds it will come to rest.

Problem • A car, starting from rest can reach 26.8m/s (60 mph) in 12 seconds. What is it’s acceleration? • A car is traveling at 26.8 m/s and slows to a stop in 4 seconds. What is the acceleration?

Problem • A driver is traveling at 40 m/s. The driver notices a police car and slows down to 25 m/s in 3.5 s.

Acceleration • Acceleration is “change in velocity” • What three parts of your car could be called accelerators?

Acceleration • Acceleration is “change in velocity” • What three parts of your car could be called accelerators? • Gas – Speeds up • Brake – Slows down • Steering wheel – Changes direction.

Some Extremely Important Equations • Δx= xf –xi = vi*t + ½ a*t2 • Δv = a * t • vf2 = vi2 + 2a Δx • Δx can be swapped with Δy if problem is vertical, • This is per textbook, I prefer the next page. These assume all initial values are zero. • These equations will be a very important part of your life for the next year.

Some Extremely Important Equations.Start a new page in Lab Notebook:Motion Equations X Vector Equations • xf = xi + vix*t + ½ acx*t2 • vfx = vix+ acx * t • acx = Δvx /Δt = (vfx –vix )/ Δt • vfx2 = vix2 + 2acxΔx (Work Energy Theorem) • Δx can be swapped with Δy if problem is vertical • These equations will be a very important part of your life for the next year.

Some Extremely Important Equations.Start a new page in Lab Notebook:Motion Equations Scalar • df = di + si*t + ½ ac*t2 • sf = si+ ac * t • ac = Δs /Δt = (sf –si )/ Δt • sf2 = si2 + 2acΔd(Work Energy Theorem) • Δx can be swapped with Δy if problem is vertical • These equations will be a very important part of your life for the next year.

Solving Kinematic Problems • NOTE: equations go • x> v > a • Or a > v > x Same for speed. • NOTE: a must be constant or you have to use your Physics year two calculus equations.

Solving Kinematic Problems • Step 1: List variables given and identify unknown. • Step 2: Identify a kinematic eq’n with those values. • Step3: Start solving.

Solving Kinematic Problems • Discuss when do you use • vfx = vix+ acx * t • vfx2 = vix2 + 2acxΔx

Problem • A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.

Another Problem • A certain gun has a muzzle velocity of 300 m/s. The barrel length is 20.32 cm. • What is the acceleration of the bullet in the barrel? • How much time does the bullet spend in the barrel?

Another Problem • An engineer is designing the runway for an airport. Of the planes which will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?

Another Problem • It was once recorded that a Jaguar left skid marks which were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s2, determine the speed of the Jaguar before it began to skid.

Another Problem • A truck covers 40 m in 8.5 s while smoothly slowing down to a final velocity of 2.8 m/s. • Find the truck’s initial velocity • Find it’s acceleration

Speed vs. Velocity