If you mean "could acceleration (the slope of velocity vs time) become infinite", the answer is yes, for an interval of zero duration having a finite integral. It is called a delta function.
http://books.google.com/books?id=SJ98Gxbhae4C&pg=PA318&lpg=PA318&dq=%22delta+function%22+velocity&source=web&ots=Fr10AiSSYn&sig=0YDJ17yF-Zi01ytI77SWVgTwkRY&hl=en
COULD ANY PART OF A SPEED LINE BECOME PERFECTLY VERTICAL ON A GRAPH?
1 answer
2 answers