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Additional general information can be obtained from [link] and the expression for a straight line, y = mx + b size 12{y= ital "mx"+b} {} .

In this case, the vertical axis y size 12{y} {} is V size 12{V} {} , the intercept b size 12{b} {} is v 0 size 12{v rSub { size 8{0} } } {} , the slope m size 12{m} {} is a size 12{a} {} , and the horizontal axis x size 12{x} {} is t size 12{t} {} . Substituting these symbols yields

v = v 0 + at . size 12{v=v rSub { size 8{0} } + ital "at"} {}

A general relationship for velocity, acceleration, and time has again been obtained from a graph. Notice that this equation was also derived algebraically from other motion equations in Motion Equations for Constant Acceleration in One Dimension .

It is not accidental that the same equations are obtained by graphical analysis as by algebraic techniques. In fact, an important way to discover physical relationships is to measure various physical quantities and then make graphs of one quantity against another to see if they are correlated in any way. Correlations imply physical relationships and might be shown by smooth graphs such as those above. From such graphs, mathematical relationships can sometimes be postulated. Further experiments are then performed to determine the validity of the hypothesized relationships.

Graphs of motion where acceleration is not constant

Now consider the motion of the jet car as it goes from 165 m/s to its top velocity of 250 m/s, graphed in [link] . Time again starts at zero, and the initial displacement and velocity are 2900 m and 165 m/s, respectively. (These were the final displacement and velocity of the car in the motion graphed in [link] .) Acceleration gradually decreases from 5 . 0 m/s 2 to zero when the car hits 250 m/s. The slope of the x vs. t graph increases until t = 55 s size 12{t="55"`s} {} , after which time the slope is constant. Similarly, velocity increases until 55 s and then becomes constant, since acceleration decreases to zero at 55 s and remains zero afterward.

Three line graphs of jet car displacement, velocity, and acceleration, respectively. First line graph is of position over time. Line is straight with a positive slope. Second line graph is of velocity over time. Line graph has a positive slope that decreases over time and flattens out at the end. Third line graph is of acceleration over time. Line has a negative slope that increases over time until it flattens out at the end. The line is not smooth, but has several kinks.
Graphs of motion of a jet-powered car as it reaches its top velocity. This motion begins where the motion in [link] ends. (a) The slope of this graph is velocity; it is plotted in the next graph. (b) The velocity gradually approaches its top value. The slope of this graph is acceleration; it is plotted in the final graph. (c) Acceleration gradually declines to zero when velocity becomes constant.

Calculating acceleration from a graph of velocity versus time

Calculate the acceleration of the jet car at a time of 25 s by finding the slope of the v size 12{v} {} vs. t size 12{t} {} graph in [link] (b).


The slope of the curve at t = 25 s size 12{t="25"`s} {} is equal to the slope of the line tangent at that point, as illustrated in [link] (b).


Determine endpoints of the tangent line from the figure, and then plug them into the equation to solve for slope, a size 12{a} {} .

slope = Δ v Δ t = 260 m/s 210 m/s 51 s 1.0 s
a = 50 m/s 50 s = 1 . 0 m /s 2 .


Note that this value for a is consistent with the value plotted in [link] (c) at t = 25 s size 12{t="25"`s} {} .

A graph of displacement versus time can be used to generate a graph of velocity versus time, and a graph of velocity versus time can be used to generate a graph of acceleration versus time. We do this by finding the slope of the graphs at every point. If the graph is linear (i.e., a line with a constant slope), it is easy to find the slope at any point and you have the slope for every point. Graphical analysis of motion can be used to describe both specific and general characteristics of kinematics. Graphs can also be used for other topics in physics. An important aspect of exploring physical relationships is to graph them and look for underlying relationships.

Questions & Answers

current economic plans (MDGS) needs
Ajijola Reply
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What is economic
Joeali Reply
What is the importance of study economics
Economic is the study of how humans make decisions in face of sacristy
economics is the study of how humans makes decision in the face of scarcity
economics is the study of human behaviour when faced with difficult situation example when goods and services are scarcity.
what is Economic
Dauda Reply
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thomas Reply
production place Price product
Criticism of elasticity
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unemployment refers to the ability for someone who is capable and willing to work but could not find a job..
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What is stock market?
JOHN Reply
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Short-run average fixed cost (SRAFC) Short-run average total cost (SRAC or SRATC) Short-run average variable cost (AVC or SRAVC) Short-run fixed cost (FC or SRFC) Short-run marginal cost (SRMC) Short-run total cost (SRTC)
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the external factor will remained constant, except the price
everything being equal
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Nikita Reply
uses of microeconomics
Adam Smith's definition of economics
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this is a situation whereby a nation's outcome or available resources are not enough to the people thereby causing scarcity
prices of Quality demanded is equal to Quality supplied
it's quantity demand and quantity supplied that's called equilibrium
they deal With prices
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elasticity is the measurement of the percentage change of one economic variable in response to a change in another
Cross Elasticity of Demand (XED) Income Elasticity of Demand (YED) Price Elasticity of Supply (PES)
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Thomas, microeconomics is the study of how consumers, workers, and firms interact to generate outcomes in specific markets
Dauda, economics is the study of people and choices. it is on one side the study of wealth and on the more important side, a part of the study if man
How does one analyze a market where both demand and supply shift?
Gabriel Reply
That's equilibrium market
but an equlibrum can appear twice on the same market... both in Movement along the Demand/supply curve of shift in the Curve
I Mean on the same curve..
how can consumer surplus be calculated
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Source:  OpenStax, Sample chapters: openstax college physics for ap® courses. OpenStax CNX. Oct 23, 2015 Download for free at http://legacy.cnx.org/content/col11896/1.9
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