# Position, velocity and acceleration vs time graphs

I'd like to draw graphs of a vehicle and I have a position vs time table.

I can set the points but how am I supposed to join them, straight or hyperbole ? If the object is accelerating which is yes then we can say velocity is decreasing and we'd draw it like this ? (not to scale, I know)

Sorry for drawing so badly

• You aren't supposed to connect them, at all. You don't know what you don't know and a diagram is not supposed to pretend that there is more information than what was used to create it. – CuriousOne Apr 8 '16 at 19:22
• @CuriousOne That's what I thought actually, but wanted to make sure – ysn_akst Apr 8 '16 at 20:10

Since only data you have is this table, you don't need to connect the points and speculate on if its graph is linear or not.You can't really know its properties with this much information. Each interval can either be linear or nonlinear on its own. Therefore, you can just leave it like this:

If you really want to sketch the velocity-time graph(again you don't have to with just this much information), you can find the average velocity for each interval and sketch it accordingly. However, take these points into consideration while sketching it:

1. What you essentially need to accomplish is to make the area under the graph at each interval to be equal to $\Delta x$ of each interval.
2. The average velocity for each interval would be $2.2$ $m/s$, $-1.4$ $m/s$, $-3.8$ $m/s$, $-3.7$ $m/s$, $-1.6$ $m/s$ respectively. However, you can't really set these values in the graph since you can't know at what point these velocities are reached. You need to know instantaneous velocity of the object at each time to accurately sketch the graph.(which will require $x(t)$ function)
3. The graph will just be an approximation and probably not even a close one.
• You're great man! Thanks! And which software did you use there ? – ysn_akst Apr 8 '16 at 20:09
• Sure thing. The software I used for the graph is Mathematica 10. You can try it or buy it(which I don't recommend unless you are using it frequently.). It is really useful and fun to work with. – user111965 Apr 8 '16 at 20:15

The position-time graph you've sketched looks roughly right (though be careful to make the scale on the vertical axis consistent). The data don't look at all linear and don't justify a straight line.

The second graph has a couple problems.

1. Is it a speed vs. time graph or a velocity vs. time graph? In what you've written you refer to velocity so, if that's what you are graphing, the last two points should be negative 1.4 and negative 3.8.
2. You got the velocity values by finding change in position divided by change in time for each interval. This gives you the average velocity during each 10 second interval. If you're plotting a graph you should be using the instantaneous velocities. The average velocity values you found will be the instantaneous velocities at some point during that 10 second interval but most likely not right at the beginning of the interval. A somewhat better approach would be to plot the 2.2 m/s point at 15 seconds, the -1.4 point at 25 seconds etc.
3. You have no reason to believe the velocity at t=0 is zero. Don't plot a point at the origin.
• 1) As at the title, it is velocity and I made a mistake there, just sleepiness 2)Yeah, I know that but as there is acceleration shouldn't velocity be inversely proportional to time squared ? 3) It's not homework actually, I set inital velocity as 0 m/s – ysn_akst Apr 8 '16 at 19:55