Question

• Find a word, number or name.The only restrictions are that it must have at least four characters, and must include at least one horizontal, vertical, angled, and curved segment each  [ example: LOVE ].
• Find parameterizations for the each characters in your word, in the xy-plane. At any time the "plotter" can only be at one location and hence the different curves making up your characters must utilize distinct time intervals!
• If F(x,y) = (xy²) i + (x²y) j is the force field acting on the plotter tip as it traces out your characters, calculate the total work done in plotting your word
• Draw typical velocity and acceleration vectors at various points along the curves of each character (on print-out).
• Calculate and graph the speed (as a function of time) along each character.
• Calculate and graph the Normal and Tangential component of the acceleration vectors (as a function of time), at least 2 locations on each character.
• Calculate and graph the curvature (as a function of time) along each character.

Answer 1

I got the acceleration as =0 for lines where velocity is uniform except at the circle so the tangential acceleration will be zero for line and the normal acceleration will be

The tangential acceleration for a circle only will be there which is

Acceleration is given as

For plotting velocity and acceleration around the letters I need some more time.