Lectures

Newton · the problem of 16651/25

Newton’s question: how fast is it changing now?

Newton wrote down a problem about quantities traced by moving bodies: when an equation links those quantities, how are their velocities linked? In modern language, how do we recover change at one instant from measurements made across time?

Think first

A falling object obeys s(t)=t². At t=2, what is its speed—not over the next second, but at that instant?

A falling object's distance and average speedThe distance is s equals t squared. Average speed from time 2 to 4.00 is 6.00 metres per second. As the interval shrinks, it approaches 4.