what is the relationship of speed and acceleartion?

Answer 1

Speed and Acceleration are related in that acceleration is the rate of change of your speed (should be velocity since you can take into account change in direction for accelerations).

The relationship can be mathematically expressed as:
dv/dt = a.

That is, the change in velocity over the change in time.

Answer 2

The speed of a body, should in fact be distinguished from velocity of the body. While velocity describes the rate of movement in space and the direction of motion, the speed is only the rate of change of displacement in space, not the direction.

Hence the question should be about the velociy and acceleration. Acceleration is the rate of change of velocity with respect to time.

Mathematically, if a body changes its velocity from v1 to v2 in time t, then the acceleration of the body during this time, a, is:

a = (v2-v1)/t

When velocity continuously changes over time this relation is expressed in calculus as:

a = d(v)/dt

Answer 3

with a constant acceleration, the speed, or more accurately velocity, can be found with the formula v=v0 at. v=velocity, v0= velocity before acceleration, a=acceleration, t=total time of the acceleration.

More generally, if you have a graph of speed versus time, the slope of the graph at a point is the instantaneous acceleration at that point.