Motion in One Dimension THE BIG IDEA Displacement

Motion in One Dimension

THE BIG IDEA! Displacement is a change of position in a certain direction, not the total distance traveled.

ONE-DIMENSIONAL MOTION • The simplest kind of motion • Objects can move forward and backward, or left and right, even up and down, but can NEVER move in two of these dimensions at the same time.

MOTION • Takes place over time • Depends upon the frame of reference of the observer • What is a “frame of reference”? • Why do we choose one? • How do we choose one? Must Know Fact! • Once you’ve decide upon a frame of reference, it MUST remain fixed for the remainder of the

DEFINITIONS • Frame of reference - A system for specifying the precise location of objects in space and time • Displacement? • Distance?

Displacement There is a distinction between distance and displacement. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path.

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)

KEEP IN MIND… • Displacement is NOT always equal to the distance traveled! • Displacement can be positive or negative! Whaaaaaa?

POSITIVE AND NEGATIVE QUANTITIES ARE JUST IDENTIFYING DIRECTIONS IN MOTION PROBLEMS!

Displacement The displacement is written: Displacement is positive. Displacement is negative.

MOTION IN ONE DIMENSION VERTICALLY • Same concept apply to the y axis! • Rockets instead of trains Change in position along y-axis = (final position on y-axis) – (initial position on y-axis)

VELOCITY AND SPEED • Velocity describes motion with both a direction and a numerical value (a magnitude, a number). • Velocity is a Vector! • Speed has NO direction, ONLY a numerical value or magnitude. • Speed is a Scalar • Average speed is equal to the total distance traveled divided by the time interval.

Average Speed/Velocity Speed: how far an object travels in a given time interval Velocity includes directional information: N, S, E, W, or left and right, even up or down

Interpreting Velocity Graphically n For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph. n 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 an object’s path. Curved lines mean? The instantaneous velocity at a given time during an acceleration can be determined by measuring the slope of the line that is tangent to that point on the position-versustime graph.

ACCELERATION • “the 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

Acceleration is the rate of change of velocity.

Acceleration is a vector, although in onedimensional motion we only need the sign. The previous image shows positive acceleration; here is negative acceleration:

Acceleration There is a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the coordinate system. Deceleration occurs when the acceleration is opposite in direction to the velocity.

JUST LIKE VELOCITY • Acceleration is a vector quantity • Has both a magnitude (velocity) AND direction • Can be positive or negative • JUST DIRECTIONAL!!!

RELATING THE TWO…

PRACTICE PROBLEMS 1. With an average acceleration of -1. 2 m/s 2, how long will it take a cyclist to bring a bicycle with an initial speed of 6. 5 m/s to a complete stop? 2. Suppose a treadmill has an average acceleration of 4. 7 × 10 -3 m/s 2. a) If the treadmill’s initial speed is 1. 7 m/s, what will its final speed be? b) How much does its speed change after 1 min?

REVIEW • Position: where are you at? • Displacement: change in position (Straight Line) • Velocity: rate of change in position with direction • Acceleration: rate of change of velocity with respect to time

MOTION WITH CONSTANT ACCELERATION • Velocity changes at a constant rate • What does displacement really depend on? • • • Acceleration Initial Velocity Time

a ΔX WITH CONSTANT Let’s see what we can do with this formula…

OUR LONELY EQUATION This is great, but what if we don’t know vf? Can we still solve for displacement?

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.

PRACTICE PROBLEMS 1. A car starts off at 10 m/s and accelerates at 1 m/s 2 for 10 seconds. What is its final velocity? 2. A car is going 30 m/s and stops in 2 seconds. What is its stopping distance for this speed? 3. A car going at 20 m/s stops in a distance of 20 m. What is its deceleration? Hint! Solve for time first…