D. Roberts PHYS 121 University of Maryland Physics 121: Fundamentals of Physics I September 15, 2006

D. Roberts PHYS 121 University of Maryland Example Problem A ball thrown by a pitcher on a women’s softball team is timed at 65.0 mph. The distance from the pitching rubber to home plate is 43.0 ft. In major league baseball the corresponding distance is 60.5 ft. If the batter in the softball game and the batter in the baseball game are to have equal times to react to the pitch, with what speed must the baseball be thrown?

D. Roberts PHYS 121 University of Maryland Average Acceleration We need to keep track not only of the fact that something is moving but how that motion is changing. Define the average acceleration by

D. Roberts PHYS 121 University of Maryland Average Acceleration Figure 2.9 Note!

D. Roberts PHYS 121 University of Maryland Instantaneous acceleration Sometimes (often) an object will move so that sometimes it speeds up or slows down at different rates. We want to be able to describe this change in motion also. If we consider small enough time intervals, the change in velocity will look uniform — for a little while at least.

D. Roberts PHYS 121 University of Maryland Technical term alert! Note that in physics we use the term “acceleration” in a technically defined way: –“acceleration” = changing velocity The object may be speeding up or slowing down or keeping the same speed and changing direction. We still say “it is accelerating.” In common speech “ acceleration ” = speeding up, “ deceleration ” = slowing down, and “ turning ”=changing direction. How many (physics) accelerators are there on your car?

D. Roberts PHYS 121 University of Maryland Equations of Motion There are a LOT of equations in the book for describing one-dimensional motion with constant acceleration –Most of them involve certain special cases or are just the same equation written in different ways –I don’t expect you to just memorize the equations Unless you really understand when they are applicable, they can lead you in to trouble! There are just two “equations” that we have used so far –They are really definitions –Everything else can be derived from them I think you will be better served in the long run if you really understand these definitions and then know how to derive on your own the other equations ALWAYS START FROM THE DEFINITIONS!

D. Roberts PHYS 121 University of Maryland Equations of Motion Definitions: –Average Velocity: –Average Acceleration: Knowing and Understanding these two definitions is key Also, relationship between position, velocity, and acceleration vs. time graphs

D. Roberts PHYS 121 University of Maryland Equations of Motion Special Case 1: Constant Motion –“Constant Motion” means velocity isn’t changing –Also means: Speed isn’t changing Direction isn’t changing Acceleration is zero Velocity could be zero, but doesn’t have to be –Position vs. time: straight line –Velocity vs. time: constant (flat) line –Acceleration vs. time: constant (flat) line at 0! Equations: If at t i =0, x i =x 0, then:

D. Roberts PHYS 121 University of Maryland Equations of Motion Special Case 2: Constant Acceleration –Acceleration isn’t changing, but isn’t necessarily zero –Velocity IS changing –Position IS changing –Position vs. time: Curved graph (parabola) –Velocity vs. time: Straight line –Acceleration vs. time: Flat (constant) line Equations: If at t i =0, v i =v 0, then:

D. Roberts PHYS 121 University of Maryland Constant Acceleration (more) Equation for position vs. time –Because the velocity is increasing or decreasing uniformly with time (straight line), the average velocity in a time interval will just be the average of the initial and final velocities:

D. Roberts PHYS 121 University of Maryland Notes: All of these derivations begin with our definitions of average velocity and average acceleration If you want to memorize these equations, you need to keep track of the special cases involved: –Constant velocity vs. constant acceleration –Are you given initial velocity (v 0 ) and initial position (x 0 )? –Form of equation could be different if you are given final position and velocity –If the initial position and/or velocity is zero, equations look different Just don’t use that form unless these conditions are true! –Not all motion begins at t=0 Bottom line: I think you are better off learning how to derive these equations, and knowing what they mean –“Knowing what they mean” means “Does it make sense” for your problem

D. Roberts PHYS 121 University of Maryland Example Look at Ch. 2, Prob. 37 –A car starts from rest and travels for 5.0 s with a uniform acceleration of +1.5 m/s 2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s 2. If the brakes are applies for 3.0 s, a)How fast is the car going at the end of the braking period? b)How far has the car gone?