Motion in One Dimension Chapter 2

Displacement and Velocity Section 2.1

Motion Diagrams Motion diagrams are a pictorial description of an object in motion. They show an object's position and velocity at the start, end, and several spots in the middle, along with acceleration (if any). http://webphysics.davidson.edu/physlet_resources/western_kentucky/MotionDiagrams.html

Drawing Motion Diagrams Draw a box or a dot representing the object at the start and end of the time of interest. Draw a box or a dot representing the object at two or three equally spaced intermediate times. If the object is traveling at a constant rate, these will be equally spaced. If it is speeding up, they will get progressively further apart. If it is slowing down, they will get progressively closer together. If the object turns around and comes back, you may want to make two motion diagrams for clarity; one from the start until the point that the object turns around, and the other from the point it turns around to the end.

Motion Motion takes place over time and depends on the frame of reference. Frame of reference is the origin, or starting point, from which motion is measured. In Physics, any frame of reference can be chosen as long as its used consistantly.

Displacement The change in position of an object. ---------------> Xi Xf Initial position Final Position Displacement = Final Position – Initial Position ∆x = xf - xi

Displacement Con’t. Displacement is not always equal to the distance traveled. If you travel to Disneyland and back home, your displacement is zero. Displacement can be positive or negative. Remember point of reference. Moving right from origin = positive Moving left = negative

Displacement Con’t.

Velocity The displacement divided by the time interval during which the displacement occurred. The unit of velocity is meters per second, m/s. To Calculate Velocity we use the equation Average Velocity = Change in position Change in time Or V=d/t

Velocity con’t. Speed and velocity are not the same. Velocity has both a magnitude and a direction Speed is just a magnitude Instantaneous velocity may not be the same as average velocity.

Sample Problem A bike travels at a constant speed of 4.0 m/s for 5.0 s. How far does it go? A car is moving down a street at 55 km/h. A child suddenly runs into the street. If it takes the driver 0.75 s to react, how far will the car travel before it begins to slow down. What is the speed of a car if it can travel 425 miles in 5 hours?

Determining Velocity From a Graph For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph. the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity. Object 1: positive slope = positive velocity Object 2: zero slope= zero velocity Object 3: negative slope = negative

Homework for Today P 44 Sample Problem A 1 – 6 P 47 P 68 1 – 11

Acceleration Section 2.2

Acceleration The rate of change of velocity with respect to time. Average Acceleration = Change in velocity time required for change a = ∆v = vf – vi ∆t tf – ti Accleration has the units of meters per second per second or m/s2

Sample Problem A race car’s velocity increases from 4.0 m/s to 36 m/s over a 4.0 s span. What is the average acceleration? Find the uniform acceleration that causes a car’s velocity to change from 32 m/s to 96 m/s in a 8.0 s period? Determine the final velocity of a proton that has the initial velocity of 2.35 x 105 m/s and then is accelerated uniformily in an electric field at the rate of -1.10 x 1012 m/s2 for 1.50 x 10-7s.

Acceleration con’t. Acceleration has direction and magnitude. Can an object accelerate with out a change in speed? Velocity?

Acceleration Consider a train moving to the right, so that the displacement and the velocity are positive. The slope of the velocity-time graph is the average acceleration. When the velocity in the positive direction is increasing, the acceleration is positive, as at A. When the velocity is constant, there is no acceleration, as at B. When the velocity in the positive direction is decreasing, the acceleration is negative, as at C.

Velocity and Acceleration

Motion with Constant Acceleration When velocity changes by the same amount during each time interval, acceleration is constant. The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown on the next slide. These equations apply to any object moving with constant acceleration. These equations use the following symbols: x = displacement vi = initial velocity vf = final velocity t = time interval

Equations for Constantly Accelerated Straight-Line Motion

Sample Problems A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and breaking system, and comes to rest 5.5 s later. Find the distance that the car travels during breaking. A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?

Today’s Work P 49 Practice B 1-5 P 53 Practice C 1-4 P 55 Practice D 1-4 P 58 Practice E 1-6 P 59 Section Review 1-6 P 69 Chapter Review 12 - 25