Chapter 2 Motion in 1 Dimension

1 Dimension What does motion in one dimension mean?

1 Dimension What does motion in one dimension mean? Traveling in one direction. Such as N, E, Up, Left **Large Ball example**

Positive and Negative Directions North (up) East (right) Negative South (down) West (left)

Displacement v. Distance Remember: Displacement is the length of the straight path from final to initial position Displacement = change of position = Δx Final position – initial position = Xf - Xi Δx = Xf - Xi

Motion As an object is moving, it not only has a initial and final location/position. It also has an initial and final time that the object traveled. Xi Xf

Average Velocity Average Velocity = Δx / Δt = (xf - xi)/(tf – ti) Can Average Velocity be Negative?

Average Velocity v. Average Speed Velocity v. Speed Speed has a distance traveled Velocity has a displacement traveled and a direction. Average Velocity v. Average Speed Average speed = (distance traveled) / (Δt) Never consider a car going a negative speed…

Average Velocity Average Velocity = What would the Average Velocity of the particle over the given interval?

Average Velocity The equation for Average Velocity is very similar to another graph formula, which one? Average Velocity = Slope = m = (rise/run) Δy = (y2 – y1) Δx (x2 – x1)

Chapter 2.2 Motion in 1 Dimension

Consider a Car A car driving at a constant 30mph to the west. Can you determine the final location of the car given a time interval?

Constant Velocity The mathematical representation of this situation is the equation. Let ti = 0 and the equation becomes: xf = xi + vx t (for constant vx)

Consider a Car A car is seen stopped at a street light then again going 30mph to the west. Did the car change velocity? How?

Acceleration The rate at which velocity changes over time; an object accelerates if its speed, direction, or both changes. Average Acceleration = change in velocity change in time

Acceleration If acceleration is in the same direction of the velocity then it is speeding up. In this case velocity is (+ or -)? Acceleration? Velocity Acceleration

Acceleration If they are in different directions the object will slow down. In this case velocity is (+ or -)? Acceleration? Velocity Acceleration

Notes Vi a + - - or + Motion Speeding up Slowing down Constant velocity - or + Speeding up from rest At rest

Motion with a Constant Acceleration What does this mean? Is there still motion occurring? Is the velocity increasing or decreasing?

Unit 2.3

Free Fall The motion of a body when only the force due to gravity is acting on the body. Which of the following is free fall: An object thrown off of a roof. An object released from a bridge. An object moving towards the ground after being thrown vertically.

ag or g Gravity Acceleration due to gravity is written as: ag: general connotation g: on Earth’s surface g = 9.81m/s2 = ___ ft/s2 Solve the conversion.

Gravity As you can see the images of the ball get closer together as the ball moves up. WHY? What happens when the ball is at its highest point?

Gravity is taking place as an object moves up and moves down. Velocity Acceleration Acceleration Velocity

Free Fall Δy

Δy= ½(vi + vf)Δt vf = vi + gΔt Δy= viΔt + ½a(Δt)2 vf2=vi2 + 2aΔy Formulas Displacement with unknown constant acceleration: Δy= ½(vi + vf)Δt Final velocity with constant acceleration: vf = vi + gΔt Displacement with known constant acceleration: Δy= viΔt + ½a(Δt)2 Final velocity after any displacement vf2=vi2 + 2aΔy