AP Physics1

Introduction to Kinematics Graphs

Background Knowledge:

Kinematics graphs are graphs of the motion measurements of an object graphed as a function of time. This means that the vertical axis is the motion measurement and time is the horizontal axis. The physicist must gain literacy in observing these graphs. From observing these graphs, the physicist must be able to interpret precisely how the object behaved in real life. Building this skill requires practice.

There are three main quantities that can be graphed on the vertical axis:

  • Position
  • Velocity
  • Acceleration

By now you should know that:

  • Velocity is the rate of change of position per unit time.
  • Acceleration is the rate of change of velocity per unit time.

A sports car that can go from 60 mph to 70 mph in 3 seconds has an acceleration that we call “a”. Convince yourself that a in this example is a=3.33 mi/hr/s. (Exercise: convert these 3.33 mi/hr/s to the units of m/s2.)

The following are also true:

  • By taking the slope of the position versus time graph, you will get the velocity.
  • Similarly, if you take the slope of the velocity versus time graph, you get ______

In the following exercise, you will be analyzing graphs by:

  • Analyzing their vertical values
  • Analyzing their slopes
  • Analyzing the amount of area bounded by the graph and the t axis. This is called finding the “area under the graph” even though sometimes you are calculating the area above the graph.

Event to Measure:

Consider a vehicle moving in some direction but also subject to a steady force that pushes it in a direction opposite to the direction of its initial motion. You see this motion happen on Interactive Physics. The following details must be understood:

  • The starting instant is defined as the time at which measurement formally began.
  • At the starting instant, the object was already in motion and the person that shoved the car has already let go.
  • At this starting instant, the steady force is already acting.
  • The steady force being referred to here is NOT the pusher’s hand, whoever it was who pushed the vehicle in the first place.
  • The steady force is external to the object. An object cannot exert a force on itself, so get that straight now. The initial velocity is in no way derived from the external force. They are entirely independent starting conditions. (Of course, later velocities will be influenced by the external force.)
  • The initial velocity of the object exists entirely independent of the external force. If the external force had not been there, motion would have continued with an unchanging velocity equivalent to the initial velocity.
  • In general, no reason is required for the existence of the initial velocity.
  • The existence of the initial velocity does NOT mean that there is a force acting in that direction. (If this fact confuses you in some way, you study “Newton’s First Law” to understand it. It’s in Chapter 4 of your textbook.)

Find your name and use the assigned mass and external force values:

Mass / Force
(kg) / (N)
Bidondo Yore / 1.6 / 11
Bottlik-Pierry / 2 / 12
Buchanan / 2.4 / 16
Burda / 2.8 / 14
Chon / 3.2 / 20
Davis / 3.6 / 16
Doub / 4 / 17
Frazier / 4.4 / 33
Fukuyama / 4.8 / 18
Glaser / 5.2 / 32.5
Irish / 4 / 20
Isozaki / 4 / 21
Kao / 4 / 22
Kim / 4 / 23
Lauro / 4.8 / 25
Lucas / 5 / 26
Mardesich / 5.4 / 27
Millman / 5.8 / 28
Munoz / 6.2 / 29
Patel / 6.6 / 30
Sun / 7 / 31
Tahbaz / 7.4 / 32
Tsai / 7.8 / 33
Usui / 8.5 / 34
Wang, Andrew / 8.9 / 35
Wang, William / 9.3 / 36
Wyrwitzke / 9.7 / 37
Zhang / 10 / 38

Data:

Record position versus time for as many instants as you like that extend at least until the vehicle is to the right of where it started by a distance of ½D. What is D? D is the symbol given to the distance to the left of where it started that the object had achieved at the instant it changed motion direction from leftward to rightward.Also record velocity versus time for this same time domain.

Hypothesis:

Just from seeing the motion, NOT by carefully analyzing data, write down your best guesses for the times of the following: When is the acceleration positive? When is it negative? When is it zero?

Analysis:

  1. Create a graph of position, x, versus time, t.
  2. From the graph, estimate the time when the car came to rest.
  3. Do a numerical calculation of a bunch of instantaneous velocities as I taught you in class.
  4. Take two randomly chosen rows of the velocity chart and perform a = v/t on them, and arrive a single answer for a.
  5. Create a graph of instantaneous velocity versus time. Draw a best-fit line on it.
  6. Measure the slope of the v vs. t graph, and compare this slope to the answer to #4.
  7. Write down the equation of the velocity line using the y=mx+b idea. No, wait, it has to be v = mt + b, and the m and the b must include proper units.
  8. Do your hypothesis guesses again to see if your common sense visualization of acceleration has changed.

Area under the graph:

Follow your teacher’s instructions in class for this part.

Final Questions: Was the car’s acceleration ever zero? Was the acceleration constant in direction? Was the acceleration constant in sign? Please state the car’s determined acceleration value. The experiment’s objective was to state as many true things about the acceleration as possible and to back that up with the numerical evidence you calculated. You are concluded with this write-up when you have told as much AS POSSIBLE about the acceleration and have defended it. That is what is meant by conclusion.