Non-Constant Velocity Motion with Non-Constant Velocity

How can we describe the motion of our car traveling down a ramp? What trends do you notice?

Analysis of Position-vs-Time Graph Object’s velocity is increasing, evidenced by a larger change in position during later time intervals For an object that do not travel at constant velocity, the slope of its position-vs-time graph is not constant

Average Velocity: Graphically The slope of a line connecting two points represents the average velocity of the object between two moments in time.

Instantaneous Velocity: Graphically The slope of the tangent line represents the instantaneous velocity of the object at any one instant in time

Velocity vs Time Graphs The vertical axis represents the object’s velocity as a function of time.

Interpreting v-t graphs Describe what each of the following v-t graphs represents about the moving object. (a) (b) (c)

Find the Mathematical Function for this graph 0 1 2 3 4 5 6 7 8 6 5 4 3 2 1 v0 a is acceleration vi is the initial velocity

Acceleration Acceleration (a) – a vector that represents the rate of change of an objects’ velocity Acceleration only occurs if its velocity is changing: Speeding up Slowing down Changing direction

Acceleration Equation: Units: Same as slope on a v-t graph!

What would be the displacement of the object in the 8 seconds? 0 1 2 3 4 5 6 7 8 6 5 4 3 2 1 Average Velocity

What are we really finding about the graph when we find displacement What are we really finding about the graph when we find displacement? (Think geometry) 0 1 2 3 4 5 6 7 8 6 5 4 3 2 1 8 s 4 m/s Area!

What would be the displacement of the object in the 8 seconds? 0 1 2 3 4 5 6 7 8 6 5 4 3 2 1

What are we really finding about the graph when we find displacement What are we really finding about the graph when we find displacement? (Think geometry) 0 1 2 3 4 5 6 7 8 6 5 4 3 2 1 8 s c Area! 4 m/s

How would you find the displacement? 3m/s Positive Area! 6 s Negative Area! 12 s -3m/s

Displacement from a v-t graph Displacement is the area under a velocity vs. time graph Area is positive above t-axis Area is negative below t-axis

Making Connections .

Making Connections

Making Connections

Motion Quiz Vectors vs. Scalars Distance vs. Displacement Speed vs. Velocity Interpreting Distance vs Time graphs: Find displacement over a certain time Find velocity at a certain time Average velocity for trip What variable represents the slope of a line Interpreting Velocity vs Time graphs Velocity at a certain time Acceleration at a certain time Displacement over a certain time