Uniform Motion t (s) x (cm) v (cm/s) 0.0 1.0 5.0 5 2.0 10.0 3.0 15.0 0.0 1.0 5.0 5 2.0 10.0 3.0 15.0 4.0 20.0 25.0 6.0 30.0 7.0 35.0 8.0 40.0

Non-uniform motion t = 1 s t = 3 s t = 0 t = 2 s t = 9 s t = 4 s

What is the velocity at t = 5.5 s? All we know from the given data is the average velocity between t = 5.0 and t = 6.0 s. Measure the object’s position at a smaller time interval, like t = 5.4 s and t = 5.6 s. Better yet, use t = 5.49 s and t = 5.51 s. The velocity at the instant t = 5.5 s is approximately equal to the average velocity during a small time interval from t = 5.49 s to t = 5.51 s. But the best we can do with the given data is guess. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Instantaneous Velocity The velocity at an instant of time is called instantaneous velocity. It is approximately equal to the average velocity measured during a very small time interval.

Position vs. time graph t (s) x (cm) 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Position vs. time graph t (s) x (cm) 0.0 1.0 0.5 2.0 2.2 3.0 5.0 4.0 0.0 1.0 0.5 2.0 2.2 3.0 5.0 4.0 8.8 13.8 6.0 19.9 7.0 27.2 8.0 35.4 9.0 45

Position vs. time graph -Slope of a tangent line on an x vs. t graph is instantaneous velocity. -Sign of slope (pos or neg) is direction of motion. -How slope changes tells you whether it is speeding up or slowing down.

Example Describe the motion of the object whose x vs. t graph is shown below.

Example Describe the motion of the object whose x vs. t graph is shown below.

Velocity vs. time graph t (s) x (cm) v (cm/s) 0.0 1.0 0.5 2.0 2.2 1.8 0.0 1.0 0.5 2.0 2.2 1.8 3.0 5.0 2.8 4.0 8.8 3.8 13.8 6.0 19.9 6.1 7.0 27.2 7.3 8.0 35.4 8.2 9.0 45 9.6

Velocity vs. time graph t (s) x (cm) v (cm/s) 0.0 1.0 0.5 2.0 2.2 1.8 0.0 1.0 0.5 2.0 2.2 1.8 3.0 5.0 2.8 4.0 8.8 3.8 13.8 6.0 19.9 6.1 7.0 27.2 7.3 8.0 35.4 8.2 9.0 45 9.6

Velocity vs. time graph -Slope of v vs. t graph is acceleration. -acceleration is the rate that the object speeds up or slows down. -if slope is constant, then the motion is characterized by constant acceleration

Example Describe the motion of the object whose v vs. t graph is shown below.

Example Describe the motion of the object whose v vs. t graph is shown below.

Example Describe the motion of the object whose v vs. t graph is shown below.

Observations If the object’s velocity is positive and the object speeds up, its acceleration is: positive negative zero

Observations If the object’s velocity is positive and the object slows down, its acceleration is: positive negative zero

Observations If the object’s velocity is negative and the object slows down, its acceleration is: positive negative zero

Observations If the object’s velocity is positive and the object speeds up, its acceleration is: positive negative zero

Position in meters Poll Car 1 t = 0 t = 1 t = 2 t =3 t =4 Car 2 t = 0 t = 1 t = 2 t =3 t =4 Car 3 t = 4 t = 3 t = 2 t = 1 t = 0 Car 4 t = 4 t = 3 t = 2 t = 1 t = 0 1. The positions of the cars above are shown at 1 s intervals from t = 0 s to t = 4 s. Which of these cars have negative accelerations during this 4 s time period? A. Car 2 only B. Car 3 only C. Car 4 only D. Cars 2 and 3 E. Cars 2 and 4

Matching position and velocity graphs Note what is being plotted in a given graph. Describe the motion in words or with a diagram. Sketch (or match) the graph that matches the motion diagram or verbal description of the motion.

The graph at left shows a moving object’s velocity v vs clock reading t. One of the graphs below shows the object’s position x plotted vs t over the same time interval. Which one is it? v t x A x B x C t t t D E x x t t