Question

What does the slope of the curve on a distance vs time graph represent?

Answer 1

Slope of a curve Y plotted against X is mathematically given as

$slope = \frac{dy}{dx}$

now here we can see that if similarly graph is plotted against distance and time then slope is given as

$slope = \frac{dx}{dt}$

here we can say that above is ratio of small distance and very small interval of time.

so here we can say that this ratio of distance and time for very small interval of time is known as instantaneous speed of the object which is falling freely under gravity.

So here slope of the graph will represent the speed at a given instant.