Hello, I have an interesting math question.
I want my robot to move 50 cm. I want its average speed to be 3.5 cm/s. However, I want my robot to accelerate at the beginning and slow down as it approaches 50 cm. In essence, a graph of robot’s speed vs. time should be a parabola that opens down. The average value of this graph should be 3.5 cm/s.
So I’m starting with the average rate that I want. How do I generate a parabola whose average value is the rate I want? Specifically, how do I figure out the peak speed my robot should achieve?
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