PHYS 1441 – Section 004 Lecture #3 Kinematics

1. PHYS 1441 – Section 004Lecture #3 Kinematics Friday, August 29, 2008 http://www.uta.edu/physics/main/faculty/fry/ • Chapter two: Motion in one dimension • Fundamentals • Velocity and Speed (average and instantaneous) • Acceleration (average and instantaneous) • One dimensional motion at constant acceleration

2. Fundamental Ideas of Mechanics • In classical mechanics we seek to describe a system by breaking it up into point particles and treat it one point at a time: x=f(t) for all t. • In quantum mechanics we seek to describe a system by specifying it everywhere at the same time: f(x,t) for all x, t. • Relativity requires different treatment for each case above: cm, qm, rcm, rqm

3. Some More Fundamentals • Kinematics: Description of Motion without understanding the cause of the motion • Dynamics: Description of motion accompanied with understanding the cause of the motion • Vector and Scalar quantities: • Scalar: Physical quantities that require magnitude but no direction • Speed, length, mass, etc • Vector: Physical quantities that require both magnitude and direction • Velocity, acceleration, force, momentum • It does not make sense to say “I ran with velocity of 10miles/hour.” • Objects can be treated as point-like if their sizes are smaller than the scale in the problem and stay that way • Earth can be treated as a point like object (or a particle)in celestial problems • Any other examples?

4. Some More Fundamentals • Motions:Can be described as long as the position is known at any time (or position is expressed as a function of time) • Translation: Linear motion along a line • Rotation: Circular or elliptical motion • Vibration: Motion which reverses itself repeatedly • Dimensions • 0 dimension: A point • 1 dimension: Linear drag of a point, resulting in a line  One-dimensional motion need not be on a straight line • 2 dimensions: Linear drag of a line resulting in a surface • 3 dimensions: Perpendicular Linear drag of a surface, resulting in a stereo object

5. Displacement, Velocity and Speed One dimensional displacement is defined as: Displacement is the difference between initial and final positions of motion and is a vector quantity Average velocity is defined as: with similar expressions for y and z components in 3 dim. Average speed: For average values, speed and velocity are very different.

6. Let’s call this line the X-axis +15m +5m +10m -5m -10m -15m Difference between Speed and Velocity • Let’s take a simple one dimensional translation that has many steps: Let’s have a couple of motions in a total time interval of 20 sec. Total Displacement: Average Velocity: Total Distance Traveled: Average Speed:

7. Example 2.1 The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x1=50.0m to x2=30.5 m, as shown in the figure. What was the runner’s average velocity? What was the average speed? • Displacement: • Average Velocity: • Average Speed:

8. Instantaneous Velocity and Speed • Can average quantities tell you the detailed story of the whole motion? • Instantaneous velocity is defined as: • What does this mean? • Displacement in an infinitesimal time interval • Mathematically: this is slope or derivative of x(t) wrt t • Instantaneous speed is the size (magnitude) of the velocity vector: *Magnitude of vectors is expressed in absolute values

9. Position x1 2 3 1 x=0 time t=0 t1 t2 t3 Position vs Time Plot It is useful to understand motions to draw them on position vs time plots. • Running at a constant velocity (go from x=0 to x=x1 in t1, Displacement is + x1 in t1 time interval) • Velocity is 0 (go from x1 to x1 no matter how much time changes) • Running at a constant velocity but in the reverse direction as 1. (go from x1 to x=0 in t3-t2 time interval, Displacement is - x1 in t3-t2 time interval) Does this motion physically make sense?