Scalar versus Vector Scalar - magnitude only (e.g. volume, mass, time) Vector - magnitude & direction (e.g. weight, velocity, acceleration)
Pictorial Representation 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” This arrow could represent a vector of magnitude 5 point to the “left”
Distance & Displacement 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 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 The distance is twice the height The displacement is zero
B A C 5 m 4 m 3 m You walk from A to B to C. Your distance traveled is 7m Your displacement form A is 5 m
Velocity & Speed 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.
Instantaneous Speed is the speed at any specific instance Average Speed is the total distance covered divided by total time Types of Speed
Speed 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 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 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 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 t i = 0
Velocity continued Direction will be the same as the direction of the displacement (time interval is always positive) – + or - is sufficient Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.) – Other units may be given in a problem, but generally will need to be converted to these
Speed vs. Velocity 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 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 Uniform velocity is constant velocity The instantaneous velocities are always the same – All the instantaneous velocities will also equal the average velocity
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, 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…
Acceleration Change in velocity divided by the change in time
Acceleration 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 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 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 Uniform velocity (shown by red arrows maintaining the same size) Acceleration equals zero
Relationship Between Velocity & Acceleration 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 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 Used in situations with uniform acceleration
Kinematic Equations - Ex #1 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 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 #2 A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 meters. What is the car’s final velocity?
Kinematic Equations - Ex #2 - Ans A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 meters. What is the car’s final velocity?
Kinematic Equations - Ex #3 A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 sec. How far does the car travel?
Kinematic Equations - Ex #3 - Ans A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 sec. How far does the car travel?
Galileo Galilei 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 All objects moving under the influence of gravity only are said to be in free fall – 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 Symbolized by g g = 9.81 m/s 2 g is always directed downward – 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 Initial velocity is zero Let up be positive Use the kinematic equations – Generally use y instead of x since vertical Acceleration is g = -9.81 m/s 2 v o = 0 a = g
Free Fall – an object thrown downward a = g = -9.81 m/s 2 Initial velocity ≠ 0 – With upward being positive, initial velocity will be negative v o 0 a = g
Free Fall - example If a rock is dropped from a building, and it takes 18 seconds to reach the ground, how tall is the building?