Speed vs. VelocityVelocity, 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. VelocityVelocity, 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 * 107 s = 3.0 * 104 m/s

• What is the velocity?

• Displacement / time

• 3.0 * 1011 m / 1.6 * 107 s = 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 * 107 s = 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

15 m

17 m

23 m@ 49 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 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

t

vv

tt

vv

t

va if

if

if

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 = vi

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

•xf = xi + vix*t + ½ acx*t2

•vfx = vix + acx * t

•acx = Δvx / Δt = (vfx –vix )/ Δt

•vfx2 = vix

2 + 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 = si

2 + 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 = vix

2 + 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.

• 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

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?

• 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

Another Problem