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 v x = Δx/Δt and v y = Δy/Δt For those of you in calculus: v x = dx/dt and v y =dy/dt

Question: The Earth is 1.5 * meters from the sun. A year is 3.2 * 10 7 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 * meters from the sun. A year is 3.2 * 10 7 seconds. If the orbit is a perfect circle, what is the speed of the earth over six months? Distance / time 4.7 * m / 1.6 * 10 7 s = 3.0 * 10 4 m/s What is the velocity? Displacement / time 3.0 * m / 1.6 * 10 7 s = 1.9 * deg

Question: The Earth is 1.5 * meters from the sun. A year is 3.2 * 10 7 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 * meters from the sun. A year is 3.2 * 10 7 seconds. If the orbit is a perfect circle, what is the speed of the earth over one year? Distance / time 9.4 * m / 3.2 * 10 7 s = 3.0 * 10 4 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 = m 17 m deg

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 a x = Δv x /Δt y vector a y = Δv y /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 d 2 x/dt 2 average

Acceleration Units – since it’s velocity per time Or

Acceleration If an object starts at rest, and has an acceleration of 1 m/s 2, 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= v f – v i ) v f = v i + 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= x f –x i = v i *t + ½ a*t 2 Δv = a * t v f 2 = v i 2 + 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 x f = x i + v ix *t + ½ a cx *t 2 v fx = v ix + a cx * t a cx = Δv x / Δt = (v fx –v ix )/ Δt v fx 2 = v ix 2 + 2a cx Δx (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 d f = d i + s i *t + ½ a c *t 2 s f = s i + a c * t a c = Δs / Δt = (s f –s i )/ Δt s f 2 = s i 2 + 2a c Δd (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 v fx = v ix + a cx * t v fx 2 = v ix 2 + 2a cx Δx

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.

A certain gun has a muzzle velocity of 300 m/s. The barrel length is 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/s 2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?

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 m/s 2, 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 Another Problem