What is relationship between force and acceleration?

Force and acceleration are inseparable in physics. Acceleration occurs only when a force acts on a mass. The larger the force, the bigger the acceleration; the larger the mass, the smaller the acceleration for the same force.

From a practical perspective, when designing vehicles or machines, engineers must consider how much force will be needed to achieve a desired acceleration. This is a direct application of Newton's Second Law. For reference, see Physics Classroom.

Newton's Second Law tells us that the acceleration of an object depends directly on the net force applied and inversely on its mass. In formula terms, F = ma. So if you push harder, the object speeds up more.

Imagine pushing a heavy cart versus a light cart. With the same force, the lighter cart accelerates faster. This simple observation is exactly why force and acceleration are linked mathematically through the object's mass.