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'Ramping it Up' printed from https://nrich.maths.org/
You might think about the graphs in terms of gradients.
You could consider replacing the vertical lines by very steep
gradient lines.
To relate the problem to acceleration, recall that the acceleration
is the second derivative of the
position.
Don't forget that you are not allowed to have 'infinite' values on
a graph.
This problem introduces the
mathematics behind 'step functions' and 'Dirac delta'
functions.