Question

What is the meaning of the gradient of distance time graph?

Answer 1

By definition, the gradient of distance-time graph is the derivative of distance with respect of time:

$$K = \dfrac{ds}{dt}$$

In case of rectilinear motion (and only in this case) this quantity is also equal to the projection of the velocity of the object:

$$v = \dfrac{ds}{dt}$$

Answer. Projection of the velocity of the object (in case of rectilinear motion).