Motion Some Motion Terms l Distance Displacement l
- Slides: 45
Motion
Some Motion Terms l. Distance & Displacement l. Velocity & Speed l. Acceleration l. Uniform motion l. Scalar. vs. vector
Scalar versus Vector l l Scalar - magnitude only (e. g. volume, mass, time) Vector - magnitude & direction (e. g. weight, velocity, acceleration)
Pictorial Representation l An arrow represents a – – vector Length = magnitude of vector Direction = direction of vector
Pictorial Representation This arrow could represent a vector of magnitude 10 point to the “right” l This arrow could represent a vector of magnitude 5 point to the “left” l
Distance & Displacement l l l Distance is the actual distance traveled. Displacement depends only on Start & Finish line Displacement is the distance traveled , in a certain direction.
Displacement Isn’t Distance l The displacement of an object is not the same as the distance it travels – Example: Throw a ball straight up and then catch it at the same point you released it l l The distance is twice the height The displacement is zero
Distance & Displacement
Distance & Displacement B 3 m A 4 m C 5 m You walk from A to B to C. Your distance traveled is 7 m Your displacement form A is 5 m
Velocity & Speed l l l Velocity is the displacement traveled in a certain time. Speed is the distance traveled in a certain time. Velocity is speed in a given direction.
Types of Speed l l Instantaneous Speed is the speed at any specific instance Average Speed is the total distance covered divided by total time
Speed l The average speed of an object is defined as the total distance traveled divided by the total time elapsed – Speed is a scalar quantity
�Velocity l The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed – Velocity is a vector quantity
Speed, cont l l l Average speed totally ignores any variations in the object’s actual motion during the trip The total distance and the total time are all that is important SI units are m/s
Velocity l l l It takes time for an object to undergo a displacement The average velocity is rate at which the displacement occurs generally use a time interval, so let ti = 0
Velocity continued l l Direction will be the same as the direction of the displacement (time interval is always positive) – + or - is sufficient – Other units may be given in a problem, but generally will need to be converted to these Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust. )
Speed vs. Velocity l l Cars on both paths have the same average velocity since they had the same displacement in the same time interval The car on the blue path will have a greater average speed since the distance it traveled is larger
Speed vs. Velocity l l l You drive from Yakima to Seattle (140 miles away) You stop in Ellensburg for a 2 hr lunch with a friend. Your total driving time is 2 hours
Uniform Velocity l l Uniform velocity is constant velocity The instantaneous velocities are always the same – All the instantaneous velocities will also equal the average velocity
Velocity Example
Velocity again How fast is the plane moving in respect to the ground?
Velocity, yet again How fast is the plane moving in respect to the ground?
Velocity (finally) How fast is the plane moving in respect to the ground?
Velocity again (? ? ) How fast is the plane moving in respect to the ground?
Velocity - the last time How fast is the plane moving in respect to the ground?
(Last) Velocity… How fast is the plane moving in respect to the ground?
Acceleration l Change in velocity divided by the change in time
Acceleration l l l Changing velocity (non-uniform) means an acceleration is present Acceleration is the rate of change of the velocity Units are m/s 2 (SI), cm/s 2 (cgs), and ft/s 2 (US Cust)
Average Acceleration l l l Vector quantity When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing
Instantaneous & Uniform Acceleration l l The limit of the average acceleration as the time interval goes to zero When the instantaneous accelerations are always the same, the acceleration will be uniform – The instantaneous accelerations will all be equal to the average acceleration
Relationship Between Acceleration & Velocity l l Uniform velocity (shown by red arrows maintaining the same size) Acceleration equals zero
Relationship Between Velocity & Acceleration l l Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing (red arrows are getting longer) Positive velocity and positive acceleration
Relationship Between Velocity & Acceleration l l Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting shorter) Velocity is positive and acceleration is negative
Kinematic Equations l Used in situations with uniform acceleration
Kinematic Equations - Ex #1 l A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 seconds. What is the car’s final velocity?
Kinematic Equations - Ex #1 - Ans l A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 seconds. What is the car’s final velocity?
Galileo Galilei l l l 1564 - 1642 Galileo formulated the laws that govern the motion of objects in free fall Also looked at: – – Inclined planes Relative motion Thermometers Pendulum
Free Fall l All objects moving under the influence of gravity only are said to be in free fall – l l Free fall does not depend on the object’s original motion All objects falling near the earth’s surface fall with a constant acceleration The acceleration is called the acceleration due to gravity, and indicated by g
Acceleration due to Gravity l l l Symbolized by g g = 9. 81 m/s 2 g is always directed downward – l toward the center of the earth Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion
Free Fall – an object dropped l l l Initial velocity is zero Let up be positive Use the kinematic equations – l Generally use y instead of x since vertical Acceleration is g = -9. 81 m/s 2 vo = 0 a=g
Free Fall – an object thrown downward l l a = g = -9. 81 m/s 2 Initial velocity ≠ 0 – With upward being positive, initial velocity will be negative vo 0 a=g
Free Fall - example l If a rock is dropped from a building, and it takes 18 seconds to reach the ground, how tall is the building?
Free Fall - answer • What do we know?
Free Fall - answer
Motion l The End
- How is distance different from displacement
- Single displacement vs double displacement
- John drove south 120 km at 60 km/h
- Two students walk in the same direction
- Displacement vs distance
- Distance vs displacement
- Distance and displacement
- How is distance different from displacement
- Distance vs displacement symbol
- Displacement is distance combined with
- Scalar and vector venn diagram
- Displacement vs distance traveled
- Displacement is distance combined with
- Chapter 11 distance and displacement
- Distance vs displacement
- Distance vs displacement
- Distance is a scalar
- Distance vs. displacement
- Distance vs. displacement
- Comic strip showing uniformly accelerated motion
- Distance vs displacement
- Distance vs. displacement
- Distance and displacement examples
- Horizontal
- Angular displacement
- Polynomial classification
- Combining like terms practice
- They say it only takes a little faith
- God when you choose to leave mountains unmovable
- Cake countable or uncountable noun
- What are some contact forces and some noncontact forces?
- Some say the world will end in fire some say in ice
- Some say the world will end in fire some say in ice
- Some trust in horses
- The ratio of input distance to output distance
- The motion of a projectile is often studied in terms of
- When an object moves, it acquires
- Total distance traveled
- Distance divided by time
- Distance time graph for uniform motion
- Projectile motion horizontal distance
- Types of range of motion
- Simple harmonic motion
- An object in motion stays in motion
- Chapter 2 motion section 1 describing motion answer key
- Measuring motion