Presentation on theme: "Chapter 2 Motion in One Dimension"— Presentation transcript:
1 Chapter 2 Motion in One Dimension Section 1Displacement and Velocity
2 MotionMotion happens all around us in different directions and different speeds.One – dimensional motion is the simplest form of motion.Example : Commuter train can move only forward and backward along the straight track.
3 Motion Motion takes place over time and depends on frame of reference. Frame of Reference – what you use to measure changes in position.
4 Frame of ReferenceFrame of reference is basically what you are using to measure changes in position of an object.If an object is at rest (not moving), its position does not change with respect to a frame of reference.As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called the displacement of the object.
5 Displacement Displacement is a change in position. Displacement = final position – initial position.Displacement is not always equal to the distance traveled.Displacement can be positive or negative!in your book (unless stated otherwise) RIGHT & UP will be considered positive and LEFT & DOWN will be considered negative.
6 DisplacementDisplacement is not always equal to the distance traveled.
7 Displacement Displacement can be positive or negative. There are only two directions to move on X axis and two to move on Y axisRight : Positive Left : NegativeUp: Positive Down : Negative
9 VelocityAverage Velocity is displacement of an object (Δx) divided by time interval (Δt).Equation : vavg = Δx = xf-xiΔt tf-tiAverage Velocity can be positive or negative depending on the sign of the displacement.If displacement is negative, avg. velocity is negative.Time interval is always positive
14 The motion of an object moving with constant velocity will provide a straight-line graph of position versus time. The slope of this graph indicates the average velocity.The motion of an object moving with constant velocity will provide a straight-line graph of position versus time. The slope of this graph indicates the average velocity.
15 2-2 AccelerationAcceleration measures the rate of change in velocity (usually per second).Acceleration has dimensions of length divided by time squared.The units of acceleration in SI are meters per second per second.m/s2
16 Acceleration Three ways to Accelerate: Object speeding up Object slowing downObject changing direction
17 Formula for Average Acceleration Change in velocitytime required for changeORa avg = vf – vitf - ti
18 Let’s Practice with Average Acceleration... Turn to page 49 in your books and we can work on practice 2B.
19 Acceleration is Velocity/Time Acceleration has direction and magnitude.The slope and shape of a graph plotting velocity vs. time describes the object’s motion.When velocity on graph isincreasing : acceleration is positivedecreasing : acceleration is negativeconstant : there is no acceleration
22 Review - Displacement with constant uniform Acceleration Displacement depends on acceleration, initial velocity, and time.Displacement with constant uniform acceleration is equal to :ΔX = ½ (initial velocity + final velocity)(time interval)
23 Solving for Final Velocity (Vf) Final velocity depends on initial velocity, acceleration, and time.aavg = Δv = vf - viΔt tf - tiDisplacement of an object depends on initial velocity, final velocity, and time.Δx = ½ (vi + vf) ΔtHow can we solve for displacement if we don’t have final velocity?
24 Solving for Vf & Displacement By rearranging the equation for acceleration, we can find a value for the final velocity.vf = vi + aΔtTo find displacement of an object moving with uniform acceleration we substitute the above expression for vf into our displacement formula.Δx = vi Δt + ½ a(Δt)2
28 Chapter 2 One Dimensional Motion Section 3Falling Objects
29 Free Fall Free fall is acceleration due to gravity. Free fall acceleration is constant.Magnitude of free fall is 9.81 m/s2Direction of free fall is directed downward.negative direction (-)Free fall is denoted with the symbol g. (Sometimes may be ‘a’ for acceleration due to gravity)
30 Free FallIn a vacuum, in the absence of air resistance, all objects fall at the same rate.
31 What goes up must come down. What causes an object that has been thrown up into the air to come back down?Free-Fall Acceleration due to gravity is always directed downward and pulling an object towards Earth’s surface.
32 Recall Information vf2 = vi2 + 2aΔx vf2 = vi2 + 2aΔy Remember we learned about a formula that can be used to find final velocity at ANY displacement…vf2 = vi2 + 2aΔxWe use this same formula but we change x to yvf2 = vi2 + 2aΔy
33 Guided PracticeOpen books to pg. 63 Sample Problem 2F