2.8.3: Predicting Motion graphs
- Page ID
- 472512
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Predict the velocity versus time graph that would result from a position versus time graph.
- Predict the acceleration versus time graph that would result from a velocity versus time graph.
We will consider one final example of interpreting motion graphs. As you look at the position versus time graph, imagine what you will see on the velocity versus time graph. Once you have made the prediction, read the discussion and look at the actual velocity versus time graph.
Figure \(\PageIndex{1}\): Vertical position versus time graph for an object that starts by moving positive in the vertical direction before gradually slowing and then moving negative in the vertical direction while gradually speeding up.
There is no point on the position versus time graph at which the slope appears to be constant. If we look at the change in the slope as we move across the graph it seems to decrease until we get to a point where the position starts to go down instead of going up. This at first might seem similar to Figure 2.8.1.2 where the position increased and then abruptly began to decrease. However this is different in that the change in position with time is not a straight line leading up to the point where it starts to decrease. In fact, if there were more points on this graph we could see that it was a slow gradual curve with no abrupt points along the way. This is similar to what we saw in Figure 2.8.2.1. If we imagine that same trend being allowed to continue, the position would not just stop increasing, but eventually begin to decrease. This is indicative of a negative velocity. Regardless of whether the initial change in position is positive or negative, the fact that each successive interval is showing a smaller (or more negative) change in position indicates that the velocity is becoming more negative with time. Because we see a curved line for the position versus time graph, we might expect to see a straight line in the velocity versus time graph. (NOTE: We can say this is true because we are only considering constant acceleration in this text.)
The velocity versus time graph is indeed negatively sloped. Notice that the velocity values are positive at times where the position values are increasing, and becomes negative where the position values are decreasing. What does that tell us that we might expect to see in the acceleration versus time graph? Make a prediction and then read the discussion and look at the actual acceleration versus time graph.
Figure \(\PageIndex{2}\): Velocity versus time graph for an object that has a velocity decreasing at a constant slope.
When we have a straight line with a negative slope for velocity versus time, that would indicate two things about acceleration: 1) the acceleration is constant because the velocity versus time graph is a straight line, and 2) the acceleration is negative because that line has a negative slope. Graphically we indicate a constant by drawing a flat line where the acceleration does not change as the time changes. Because we are only considering motion graphs with constant acceleration for this class there are essentially three options for the acceleration versus time graph: 1) a flat line at a positive number for an object which is accelerating in the positive direction, 2) a flat line at a zero value for an object which is not accelerating, and 3) a flatline at a negative number for an object which is accelerating in the negative direction (as we see in this example.)
Figure \(\PageIndex{3}\): acceleration versus time graph for an object that has a constant negative acceleration.
You may continue to practice interpreting motion graphs in your study groups. Make a position versus time graph and then ask your study partners to make velocity versus time graphs and acceleration versus time graphs to accompany your graph.
Contributors
Curated from resources found in Introduction to Physics published by OpenStax.