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Before we begin though…..a few things When we look at a line with no numbers we are just looking at the shape, analyzing the shape of the line. Slope can help with that.
The x axis is always time, the y axis is either labeled position, velocity, or acceleration. The y axis is determined by the type of question.
When we analyze points using slope we are finding the average velocity. Average velocity – the average of all instantaneous velocities; found simply by a distance/time ratio. Instantaneous velocity - the velocity at any given instant in time. (the velocity at one specific point) Average velocity is different than instantaneous velocity. The same principle is applied with acceleration. Avg acceleration – average of all accelerations. Instantaneous acceleration – acceleration at one specific point.
Displacement vs. time graphs. Velocity vs. time graphs. Acceleration vs. time. ***Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Let’s look at the displacement vs. time graph.
aka. position vs. time graph. x. t.
The slope of the line will give you the average velocity. Slope = rise. run. = ∆ in vertical coordinates. ∆ in horizontal coordinates. Imagine that you are running a marathon and we have decided to graph your movement.
Slope = d/t = v. Since it is moving up in a straight line you have a positive constant velocity.
90s-150s – during this time your position has stayed the same. So v = 0m/s.
In this section you are moving at a faster constant velocity.
240s-300s – again finding the slope will give you your velocity. But notice it is negative. This means you turned around. So your velocity is negative.
This means the slope of the line is getting larger. Since slope = velocity you are accelerating!
● If you see any part of the happy clown s face on a graph, it is positive acceleration. ● If you see any part of the sad clown s face, it is negative acceleration.
When the line reaches zero 0 on the x-axis. The object is said to be at rest
velocity vs. time graph v t
First thing to remember. The rules are not the same for both displacement vs time and velocity vs time graphs! The lines mean different things. For the next example, the graph is from the same data (the marathon)
0s-90s – you were running at a positive constant velocity. On a v vs t graph, a flat line means constant velocity.
It is a flat line at zero, which means your velocity was zero.
150s-240s – You are running forward again. To show a faster velocity than earlier, we have a flat line that is higher than the previous one.
You are running at -3.3m/s.
300s-360s – Again, horizontal line at zero. You must have stopped.
The slope is equal to the acceleration: ∆V. Slope = = a. t.
acceleration vs. time graph
In the v vs. t graph, we showed that the slope of the line showed an increase (change) in velocity over time. ∆v / t = acceleration. Because this change in velocity over time is a constant change in velocity, that means the acceleration itself is also constant.
Acceleration that is constant is shown on a graph by a flat straight line.
X. a vs. t graph. Straight line in positive direction means the acceleration is also constant over time. v vs. t graph. Straight line in positive direction means it is increasing at a constant velocity.. x vs. t graph. Displacement getting more positive (greater) over time. If you graphed this as v vs. t it would be…
has a constant decrease of velocity over. time which is called deceleration. a vs. t graph. there is a constant negative acceleration or deceleration in the graph. X. x vs. t graph. shows a graph of an object moving backwards at a decelerating speed.
a vs. t graph. there is a constant positive acceleration in the graph. x vs. t graph. here the object is moving at. an accelerating speed towards the point of origin.
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