If we are trying to pedal a bicycle gently, we require a particular amount of effort which all of us intuitively know. However if we need to move it at a higher speed, we need to “push” it hard. Now, if we have pillion rider on the bicycle we need to put in more effort. Thus we find that the “push” is related (read proportional) to the mass as well as the increase in speed ( change is speed per unit time or acceleration ). Now the question is why we multiply mass and acceleration. Whenever we need to bring in the effect of two or more quantities simultaneously, we multiply them. We need to bring the effect of both mass and acceleration simultaneously. We also multiply things when they are related. If one (mass or acceleration) is more the other has to be proportionately less for the same force. Hence we multiply mass and acceleration to quantify our “push” and we call this quantity as a Force.
We define force,F = m * a, where m is the mass of the body and a the linear acceleration of the body on a plane.
Please be forewarned that forces exist even if there is no motion associated with it. A bridge is permanently applying a force by way of it's weight on the columns. However there is no visible motion. There will be a separate post on stationary forces.