Position, Velocity, Speed and Acceleration in GeoGebra

If you have a vector function that describes the position of a particle, you can use GeoGebra to calculate its velocity vector, its speed, its acceleration vector, and its acceleration.

GeoGebra Instruction 1

Assume you have a vector function (x(t),y(t)) that describes the position of some object.

Open GeoGebra icon View and select CAS.

Velocity Vector v(t)

1.
Enter the functions x(t) and y(t). Beware that GeoGebra doesn’t allow you to use the letters x(t) and y(t) as names for functions, so give them other names.
2.
Enter Derivative(<Expression>) and then enter the name of x(t). Press Enter. You get the x-coordinate of the velocity vector.
3.
Enter Derivative(<Expression>) and then enter the name of y(t). Press Enter. You get the y-coordinate of the velocity vector.

Speed |v(t)|

1.
First, find the velocity vector as described in the previous step.
2.
Enter

sqrt(<x-coordinate of the velocity vector n>^2

+ <y-coordinate of the velocity vector>^2)

3.
Press Enter. You get the function |v(t)| for the speed.

Acceleration Vector a(t)

1.
First, find the velocity vector.
2.
Enter Derivative(<expression>), and then enter the expression you have for the x-coordinate of the velocity vector. Press Enter. You get the x-coordinate of the acceleration vector.
3.
Enter Derivative(<expression>), and enter the expression you have for the y-coordinate of the velocity vector. Press Enter. You now get the y-coordinate of the acceleration vector a(t).

Acceleration |a(t)|

1.
First, find the acceleration vector as above.
2.
Enter

sqrt(<x-coordinate of acceleration vector>^2

+ <y-coordinate of acceleration vector>^2)

3.
Press Enter. You now get the acceleration |a(t)|.

Screenshot of GeoGebra showing computations of velocity, speed and acceleration

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