Mark Lesmeister Dawson High School Pearland ISD © Mark Lesmeister/Pearland ISD

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Ox0x0 x

 Position- Location of an object relative to an origin, e.g. x 0 = 30 m  Displacement- Change in position.  Time interval- Elapsed time between events.  Average velocity- Displacement/time  Instantaneous velocity- velocity at a particular time. (v) Ox0x0 x

 Position- Location of an object relative to an origin, e.g. x 0 = 30 m  Displacement- Change in position.  Time interval- Elapsed time between events.  Average velocity- Displacement/time  Instantaneous velocity- velocity at a particular time. (v) Ox0x0 x In the constant velocity model, v AV = v

x 0 usually refers to the position at t = 0, i.e. t 0 = 0. So, we get

x 0 usually refers to the position at t = 0, i.e. t 0 = 0. So, we get

 In the constant velocity model, the velocity is a flat line.  The displacement is given by Δx=v Δt  On a graph, the magnitude of the displacement is the area underneath the velocity graph.  What if the velocity is negative?

 One example of a changing velocity is free- fall. In the picket fence lab, we will draw graphs of the position versus time and velocity versus time for an object in free-fall.

 v vs. tx vs. t

 If the velocity is not constant, we can define the acceleration. ◦ a AV = Δv/Δt  If the acceleration is constant, we omit the subscript AV. ◦ Then the acceleration would be the slope of the v vs. t graph.

 In the constant acceleration model:

 Free fall obeys the constant acceleration formulas. ◦ That means that *at all times* during free-fall, even at the top of the motion, the acceleration is the same. ◦ The acceleration caused by gravity is 9.8 m/s 2 in the downward direction. ◦ The quantity 9.8 m/s 2 is often abbreviated g. ◦ a g = m/s 2 = -g

Holt PhysicsAP Physics C, e.g. Tipler  Equations stated in terms of intervals: ◦ Displacement ∆x ◦ Time interval ∆t ◦ v i and v f are velocities at beginning and end of interval.  Initial quantities shown with subscript “i”, as in v i.  Equations of motion give position x and velocity v as functions of time t. ◦ Initial position and velocity appear in equations. ◦ Initial time is taken to be 0, so time interval becomes just t.  Initial quantities labeled with subscript “0”, to show they were the value at time t=0.

HoltAP C  This one is not on the AP C formula chart.

 Average speed refers to the total distance covered divided by the total time elapsed. ◦ The average speed may be nonzero even when the average velocity is zero.  Instantaneous speed is the magnitude of the instantaneous velocity at a given time. ◦ The magnitude of a vector is usually shown with the same symbol as the vector, but not in boldface or with a vector symbol.

 On a West Texas highway, you come across an immigration checkpoint and apply the brakes to come to a stop. You slow down at a constant rate of 4.0 m/s 2. How far does your car travel before it comes to a stop if the initial speed of the car was 20 m/s (about 45 mph)? What if the initial speed of the car was 30 m/s?

 Based on a problem in Physics by Cutnell and Johnson, 5 th edition:  An astronaut is trying to determine the acceleration of gravity on a strange planet. The astronaut doesn’t have a meterstick, but does possess a device that launches small spheres at an initial velocity of +15 m/s, and a stopwatch. Suggest a procedure the astronaut could follow.  If the astronaut launches a sphere straight up, it takes about 20 seconds for the sphere to come back down.

 The slope of the position vs. time graph is the velocity, so ◦ A horizontal graph is zero velocity. ◦ A linear graph is constant velocity. ◦ A graph that curves upwards is increasing speed.  The slope of the velocity vs. time graph is the acceleration. ◦ A horizontal graph is zero acceleration, i.e. constant velocity. ◦ A linear graph is constant acceleration.

 When is the object: ◦ Farthest from the origin? ◦ At rest for an instant? ◦ At rest for an extended time? ◦ Moving away from the origin? ◦ At its minimum speed? ◦ Showing positive acceleration? ◦ Showing negative velocity? A B C D E F G

 The slope of a position vs. time graph is the velocity at that time.  The slope of a velocity vs. time graph is the acceleration at that time.  The area under a velocity graph is the displacement.  The equations in the constant acceleration model are