Table of Contents Position and Displacement Velocity Acceleration
Table of Contents • Position and Displacement • Velocity • Acceleration • Motion with Constant Acceleration • Falling Objects Equations for Chapter 2
One-Dimensional Motion • The simplest kind of motion • Things can move forward and backward, but not left and right
Displacement is a change of position in a certain direction, not the total distance traveled
• When things start moving, the length of a straight line drawn from the object’s initial position to it’s final position is it’s displacement • In one dimension… Change in position along x-axis = (final position on x-axis) – (initial position on x-axis) Read the TIP at the bottom of p. 41!
Equations for Chapter 2
More Equations…
Keep in mind… • Displacement is not always equal to the distance traveled! • Displacement can be positive or negative!
POSITIVE AND NEGATIVE QUANTITIES ARE JUST DIRECTIONS IN MOTION PROBLEMS!
Velocity • It is the time rate of change of displacement
Average Velocity • Average velocity is the total displacement divided by the time interval during which the displacement occurred.
Velocity and Speed • Velocity describes motion with both a direction and a numerical value (a magnitude). • Speed has no direction, only magnitude. • Average speed is equal to the total distance traveled divided by the time interval.
Velocity and Speed
+’s and –’s are Directional!
Interpreting Velocity Graphically • For any position-time graph, we can determine the average velocity by drawing a straight line between any two points the graph. • If theon velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity. Object 1: positive slope = positive velocity Object 2: zero slope= zero velocity Object 3: negative slope = negative velocity
Instantaneous Velocity The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path. The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.
Acceleration is • “rate of change of velocity with respect to time” • How much does your velocity change, and how fast does this happen? a is measured in m/s 2
Just like Velocity • Acceleration is a vector quantity • Has both a magnitude (speed) AND direction • Can be positive or negative • JUST DIRECTIONAL!!!
Graphs can tell us things
Review of last week • Position: where are you at? • Displacement: change in position • Velocity: rate of change in position
Velocity vs. Time
v with constant a Rearranging the equation tells us that…
Finding displacement Let’s substitute our new equation in for vf … …and simplify the new equation.
One last equation…
One Dimensional Motion
Terms Displacement vs. Distance Displacement: Change in position (vector) • Distance: How far an object has travelled (scalar) • Symbol: Δx or Δx • SI Unit: meter, m
Position
Terms Velocity vs. Speed • Velocity: Rate of the change in position (vector) • Speed: Rate of distance covered (scalar) • Symbol: v or v • SI Unit: meter per second, m/s
Average Velocity
Instantaneous Velocity
Terms Acceleration vs. Acceleration • Acceleration: The rate at which velocity changes (vector) • Acceleration: The rate at which speed changes (scalar) • Symbol: a or a • SI Unit: meters per second or meters per second
Average Acceleration
Instantaneous Acceleration
Position vs. Time Graph
What are the velocities?
What are the velocities?
Average Velocity on an x-t graph
vav vs vinst on an x-t graph
x-t graph vs motion of a particle
Instantaneous Velocity on an x-t graph
Velocity vs. Time Graph • The slope of a v vs. t graph is the acceleration • The area between the curve and the horizontal axis of a v vs. t graph is the displacement
Comparison of v-t to a-t graphs
Instantaneous Acceleration vs Average Acceleration from a v-t graph
v-t graph vs motion of a particle
x-t graph vs motion of a particle with acceleration
What are the accelerations and displacements?
What are the accelerations and displacements?
Acceleration vs. Time Graph • The slope means NOTHING • The area between the curve and the horizontal axis is the change ain velocity 10 s -10 m/s/s t
Important Acceleration tells us how fast velocity changes Velocity tells us how fast position changes
Kinematics Equations (accelerated motion)
Falling Bodies, thrown up objects, and the y-direction • All things fall at the same rate (neglecting air resistance) • On earth that rate is 9. 80 m/s 2 • That rate is an acceleration • The name of that acceleration is Gravity
Object moving in y-direction
Changing Acceleration
Velocity by Integration
Position by Integration
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