Chapter 2 Motion Section 1: Describing Motion Section 2: Velocity and Momentum Section 3: Acceleration

Section 1: Describing Motion Motion occurs when an object changes its position You need a reference point to know whether an object has changed its position Think about a jet flying across a cloudless sky. Without a reference point how would you know the jet is in motion? Distance – how far an object has moved Displacement – the distance and direction of an object’s change in position from its starting point. Speed – the distance an object travels per unit time Speed is a rate Rate – any change divided by time Calculating speed: Equation: 𝒔𝒑𝒆𝒆𝒅= 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆 , or: Speed is rarely constant Think about a trip you have taken. Did you make any stops? Did you pass anyone? Average Speed is total distance divided by total time Instantaneous speed is the speed at a specific instance The speedometer in your car indicates instantaneous speed

Section 1: Describing Motion A vector is a quantity that describes magnitude and direction Displacement is vector Can be indicated using arrows Add vectors by arranging tail to tip Other vector quantities include: velocity (speed and direction) and acceleration (change in speed and direction) Example: walking to school: Video

Section 1: Describing Motion Sometimes it is useful to make a graph of distanced traveled over a period of time To make a distance/time graph: Distance is plotted on the y-axis (dependent variable) Time is plotted on the x-axis (independent variable) Each axis must have a scale that covers the range of numbers you are working with. Example: Dick, Ted, and Bill race the 4 miles to school from Bill’s house. Dick takes 3 minutes to drive to school, Bill takes 2.5 minutes, and Ted 6 minutes to drive to school. However, Ted stopped to get a cup of coffee at MiniMart; it took him 1.5 minutes to get there, the stop took 2 minutes, and the MiniMart is 1.5 miles from Bill’s house. Plot the distance/time graph for each person. Solution: Plot the individual data. The data for Dick and Bill are easy to plot as they did not stop on the way to school. Simply place a point at the appropriate coordinates and draw a straight line from (0,0) to that point. The plot for Ted is more complex as he stopped, so you have to show that period of time that he was not moving. The motion of Dick, Bill and Ted is shown to the right.

Section 2: Velocity and Momentum Sometimes just knowing the speed of something is not information. Sometimes you need to know the direction something is moving Velocity – the speed and the direction at which something is moving You use the speed equation to calculate velocity and then indicate direction of travel Direction can mean north, south, east, or west; or any indicator of direction, like: toward, away, up, down, etc. Example: A driver heads north out of Spearfish, his destination is Bowman, ND, which is 290 km away. If he arrived in Bowman 2.75 hours later, what was the driver’s average velocity?

Section 2: Velocity and Momentum You can solve for any variable in the speed equation using simple algebra. To solve for distance the solution process would look like this: To solve for “time” the solution process would look like this: Start with the speed equation: 𝑉= 𝑑 𝑡 . Multiply both sides of the equation by “t”. 𝑡 𝑉= 𝑑 𝑡 (𝑡). The “t’s” cancel and the equation becomes: 𝑡 𝑉=𝑑. Now divide both sides of the equation by “V”: 𝑡 𝑉 𝑉 = 𝑑 𝑉 . The “V’s” cancel on the left side of the equation and we are left with: 𝑡= 𝑑 𝑉

Section 2: Velocity and Momentum Example: If Matt sets the cruise control on his car at 120 km/hr, how long will it take him to travel 515 km? Example: If a driver maintained an average speed of 100 km/hr how far will she travel in 3.5 hours? Video

Section 2: Velocity and Momentum Momentum – the product of an object’s mass and velocity Momentum is related to how much force is needed to change the motion of the object Equation for momentum: momentum = mass x velocity, or: Momentum is related to an object’s mass and velocity An object with a small and high velocity can have a great deal of momentum, just as an object with a large and low velocity can have a high momentum. Law of Conservation of Momentum: Momentum of an object doesn’t change unless there is a change in the object’s mass or velocity Momentum can be transferred from one object to another Example: playing pool - The momentum lost by the cue ball equals the momentum gained by the other balls. The total momentum in the system remains constant, but is distributed differently.

Section 3: Acceleration Acceleration – the rate of change of velocity 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏= 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆 , 𝒐𝒓: 𝜶= ∆𝒗 ∆𝒕 Typically, an object is not constantly accelerating, so ∆t is the length of time the object is accelerating. Remember: Velocity has a direction component, so if the direction an object is traveling changes the object has accelerated. Example: Dan is driving west on I-90. He started driving at a rate of 104 km/hr, 15 minutes he is traveling at a rate of 120 km/hr. What was his acceleration? Notice that we had to convert time from minutes to hours so that the time units would agree.

Section 3: Acceleration Example: the Space Shuttle accelerates at 2,500 m/s2 at launch. What is the velocity of the shuttle 25 s after launch? Notes on problem-solving: Always list the known values in the problem, and indicate what variable for which you are trying to solve. Always start the solution with the correct equation Show all of the work required to solve the problem including all algebra and dimensional analysis. Write as neatly and as clearly as possible. If I cannot read what you have written I will not grade it. Typically a solution will be worth three (3) points: one (1) point for work one (1) point for dimensional analysis one (1) point for the correct answer