Graphing Basics & Velocity 8/22/11

graph = a visual display of data, usually resulting in an observable pattern line graph = a graph in which the data from two variables intersect, represented by points on the graph. line graphs always have two axis: the x-axis (horizontal) and the y-axis (vertical). Each axis should be labeled with a: variable (something measured, such as “time” passed), a unit (that the variable is measured in, such as “min”), and a scale = number range on an axis that represents the minimum and maximum values of the measured variable. the scale should fit the entire length of the graphable area, have equal-sized increments, and extend just beyond the minimum and maximum.

once the axis have been properly labeled with the variable, unit, and scale, the points can be plotted onto the graph from the info in the data table. find the first x-axis value, then find the first y-axis value. Draw a small dot (point) on the graph where those two values intersect. Continue plotting the rest of the points. Then draw a best fit line through the points. best-fit line = a line drawn through points on a line graph. These lines usually do not “connect the dots” and most likely will not touch each point, but represent the overall “pattern” in the data Sometimes a smooth curve is needed instead of straight line. Either way, do not just connect the dots!!!

now let’s try constructing a line graph! properly label the axis with the variable, unit, and scale, then plot the data points found in the data table to the right. Also, include a title for your graph. all graphs must have a title showing what was measured. Time (s) Distance (m) time (s) distance (m) distance vs. time

I. Motion you can tell that an object has moved if its position has changed against some background point that stays the same. We call this point the frame of reference. distance = a measurement of how far an object has moved. measured in meters (m), kilometers (km), or centimeters (cm) objects don’t always travel in just one direction. Sometimes they move in such a way that they end up travelling back towards their starting point. when this is the case, displacement must be measured

displacement = the distance and direction of an object’s change in position from the starting point. Always includes a directional component (such as north, sideways, at 30 , down, around a corner, etc.) the length of the runner’s displacement and the distance traveled would be the same if the runner’s motion was in a single direction. However, the runner turned around, so his displacement is 20 m north. What is the runner’s total distance?

II. Speed speed = distance traveled divided by the time interval during which the motion occurred. units for speed show a distance unit (such as meters, m) divided by a time unit (such as seconds, s) = m/s constant speed = speed that does not vary over time (like a car travelling down a highway with a non-moving speedometer). average speed = speed that varies over time (like a car travelling down a residential street with stop signs, etc.). instantaneous speed = speed of an object at a given point in time (like a radar gun measuring a car’s speed). speed = distance s = d time t speed = distance s = d time t

III. Graphing Motion speed can be determined from a distance-time graph. distance is on the y-axis, time is on the x-axis when comparing several speed lines on the same graph, the line with the most slope (closest to vertical) is the fastest. an object at rest starts at 0 distance and 0 time. let’s see if you can calculate some speeds!

Ex1: A car travelled a distance of 82.5 m in 6.4 s. What was the speed of this car? s = _________ d = _________ t = _________ Ex2: A toy train was pushed at 2.77 m/s for 0.38 s. What distance did this toy train travel? s = _________ d = _________ t = _________ ? 82.5 m 6.4 s s = d t s = 82.5 m = 6.4 s m/s 2.77 m/s ? 0.38 s s = d t t   td = s  t d = (2.77 m/s)(0.38 s) = d = 1.05 m

Velocity velocity = a quantity describing both speed and direction (also known as speed with a directional component) another way of defining velocity is “displacement over time,” since displacement includes a directional component. velocity can be positive or negative along the line of motion. For instance if north = pos, then south = neg. If clockwise = pos, then counterclockwise = neg. let’s try some velocity calculations: velocity = distance v = d time t velocity = distance v = d time t

Ex1: On a trip from Atlanta to Birmingham, a car was clocked travelling a distance of 570 m in 21.7 s. What was the velocity of this car during this time period? v = _________ d = _________ t = _________ Ex2: A train travelling south covered a distance of 65 km at 44.4 km/hr. How long was the train in motion? v = _________ d = _________ t = _________ Ex3: It takes Mrs. Rigdon 4.3 hours to arrive in PCB from Douglasville. If her average velocity was km/hr, how far away is PCB? v = _________ d = _________ t = _________