ST.JOSEPH'S HIGHER SECONDARY SCHOOL TVM-1 DEPARTMENT OF PHYSICS WELCOMES YOU

Motion in One Dimension Chapter 2 Motion in One Dimension

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

in a certain direction, not the total distance traveled The Big Idea Displacement is a change of position in a certain direction, not the total distance traveled

Read the TIP at the bottom of p.41! Displacement 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 on the graph. If the 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/s2

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 Acceleration: rate of change of velocity

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

Acceleration vs. Acceleration 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 per second or meters per second squared, m/s/s or m/s2

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 in velocity a 10 s t -10 m/s/s

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/s2 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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