PHY103 1nd EditionExam # 1 Study Guide Lectures: 1 - 6Lecture 1 (September 5)What information is given by a vector? What is the difference between distance and displacement? What is the difference between speed and velocity?A vector tells of magnitude (simple number quantities) and direction of an object. Distance is a scalar, or simple number that tells the entire distance an object has covered in a motion, while displacement is a vector quantity which tells how far an object has moved from its original position and the direction it is from the original position. Speed is a scalar quantity, combining the total distance travelled and the time the trip took. Velocity is a vector quantity, combining the displacement of an object and the time it took the object to reach that place.What is the equation for average speed? For average velocity?Average Speed (<v>) = distance covered (∆d) / duration of the trip (∆t)Average Velocity (<v>) = (final displacement-initial displacement) / change in time (∆t)Lecture 2 (September 8) How do we plot position, and velocity versus time? How do these plots relate to each other?We can plot position or velocity versus time using rectangular coordinates. By plotting position versus time in this way, we can use the slope to determine what the graph of velocity versus time would be for this motion. Average velocity is the slope (rate of change) of this plot.What then is acceleration? How could we plot this?Acceleration (<a>) = change in velocity (∆v) / change in time (∆t)We could use the plot of velocity versus time to determine what a plot of acceleration would look like, using the slope. At 7 seconds the velocity becomes 0 instantaneously, therefore the slope would be 0 although the graph shows a slope. For the slope of the acceleration plot to not be 0, the velocity plot must have a non-zero slope and the position plot must be curved to show that the object is changing position at differing time intervals, not constantly.1 2 3 4 5 6 7 8 9 10-4-3-2-10123Velocity versus TimePosition versus TimeTime (s)Speed (m/s)1 2 3 4 5 6 7 8 9 10024681012Position versus TimePosition versus TimeTime (s)Distance (m)1 2 3 4 5 6 7 8 9 1000.10.20.30.40.50.60.70.80.91Acceleration versus TimePosition versus TimeTime (s)Acceleration (m/s2)Lecture 3 (September 10)What is free-fall? What is the acceleration due to gravity? What are the two kinematic equations we can then use?Free-fall is motion under the sole influence of gravity. Therefore anything falling to the earth or held in the earth’s orbit is in free-fall. The acceleration due to gravity is -9.8 m/s2. This is constant and equal for all objects, regardless of mass. The two kinematic equations can now be used. These are:1. Xf – Xi = Vi ∆t + ½ a (∆t2), Where X= position, f= final, i= initial, V= velocity, a= acceleration, and ∆t= the change in time.2. Vf2 = Vi2 +2a (Xf – Xi), Where V= velocity, f= final, i= initial, a= acceleration, and X= position.Lecture 4 (September 12) How do we deal with motion in two directions? What do these plots tell us?Motion in two directions can be broken down into two independent directions. The x-component and the y-component. The vector created tells the latitude and longitude. The plot tells us only one piece of information: position, velocity or acceleration, not versus time. The graph looks like: To find the magnitudes of the components we can use trigonometry.Sin ᶿ = b/h cos ᶿ = a/h tan ᶿ = b/a h b h =a2(¿+b2)√¿ ᶿ aWhat is vector arithmetic? What are some of the methods?Vectors can be added and subtracted. There is the head-to-tail method, in which you line the vectors up one right after another then create the resultant vector. There is the parallelogram method in which you line both vectors up at the origin, then attach the opposite vector to the ends of each, creating a parallelogram, and draw the vector from the beginning to the point where they touch. Then there is the component method, in which you find thecomponents (x and y values) of each vector and add them together. Then finish the triangle between the sides created.How do you write vectors?Component form is A = Ax ^x + Ay ŷ ; ^x is a vector magnitude = 1 in +x direction, ŷ is a vector magnitude = 1 in the +y direction.Magnitude-angle form is A =|A|, θ degrees from the positive x axis. A and θ can be found using the trigonometric equations.Lecture 5 (September 15)What are projectiles? What is the range, time of flight and maximum height of an object?Projectiles are objects that move in two dimensions and are affected only by gravity (free-fall). The horizontal and vertical motions are independent of each other, therefore we have two sets of kinematic equations for every projectile object. One set for the x direction and one set for they direction. Range is the change in horizontal position, ∆x = Xfinal – Xinitial. Time of flight is the totaltime the projectile is in flight. The maximum height of the object is where the velocity in the y direction is equal to 0.Lecture 6 (September 17)What does relative velocity mean? What is the most common reference frame? How do we dealwith these kinds of problems?Descriptions of motion are relative to the reference frames we choose, changing reference frame does not change reality, just our description of reality. The earth is the most common reference frame and we consider it to be unmoving. The relative velocity of one object with respect to another is the difference between their velocities. To deal with these types of problems, we must add relative velocities together to get the velocity of the resultant vector. Vxz= Vxy +