Drawing Velocity Time Graphs from Position Time Graphs Uniform and Non-Uniform Motion

Think about… Sketch a position-time graph of each object listed below. Describe its slope as positive or negative, and as constant, increasing, or decreasing. A) a stone at rest B) a jogger moving steadily to the right C) a bicycle moving to the left and slowing down D) a rocket moving up at an increasing speed E) a stone falling freely with increasing speed F) a parachutist drifting down at a steady speed

Non-Uniform Motion An object does not always move at a constant speed. You may speed up or slow down. Non-uniform motion, when graphed, appears as a curve not a straight line.

Instantaneous Velocity When you are driving on the highway and you look down at your speedometer, you are traveling at + 55 km/h. At that instant in time, + 55 km/h is your instantaneous velocity. For uniform motion, your instantaneous velocity is the same as you average velocity. For non-uniform motion, your instantaneous velocity changes.

Finding Instantaneous Velocity from a Graph (Uniform Motion) To find instantaneous velocity on a uniform position-time graph, just find the average velocity for the given segment.

Finding Instantaneous Velocity from a Graph (Non-Uniform Motion) To find instantaneous velocity on a non-uniform position-time graph, draw a line that is tangent to the curve at that point. The slope is the instantaneous velocity (take the two points on the tangent from each side of the point).

http://en.wikipedia.org/wiki/Tangent

Instantaneous Velocity (Non-uniform Motion)

Worksheet

What does a v-t graph look like? Time is marked on the horizontal axis and velocity is on the vertical. Graphs that represent an object’s velocity versus its time.

What can we determine from a velocity time graph? Velocity and speed Time Acceleration Displacement and distance

What can we determine from a velocity time graph? Velocity - reading directly off the y-axis

What can we determine from a velocity time graph? Time (read off the x-axis)

What can we determine from a velocity time graph? Displacement = area under the curve NOTE: Area formulas: Arearectangle = length x width Areatriangle = ½ base x height

What can we determine from a velocity time graph? Acceleration = v/t = slope

What can you find from a v-t graph Acceleration = slope at a point on the graph (you may have to use a tangent) Average acceleration = finding the slope of a segment (use the start and end points)

Interpreting v-t graphs Horizontal lines show uniform motion (constant speed and direction). Inclined lines show change in speed or direction, or both: in other words accelerated motion.

Velocity-Time Graphs

Worksheet

How can we use d-t graphs to determine v-t graphs? Find the velocity for each section of the graph and plot it (make a list of points).

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