Introduction:
Force is defined as a push or pull that can cause an object to accelerate, decelerate, or change its direction. In the context of the given options, we will discuss the role of force in starting a stationary object and stopping a moving object.

Explanation:
To understand why force is required to start a stationary object and stop a moving object, let's analyze each option one by one.

a) To start a stationary object:
When an object is at rest, it tends to remain at rest due to its inertia. Inertia is the resistance of an object to any change in its state of motion. To overcome this inertia and initiate the motion of a stationary object, an external force needs to be applied. This force counteracts the object's inertia and provides the necessary push or pull to start its motion.

Example: Consider a car that is parked on a flat surface. To set the car in motion, the driver needs to press the accelerator pedal, which applies a force to the wheels. This force overcomes the inertia of the car, allowing it to start moving.

b) To stop a moving object:
When an object is in motion, it tends to stay in motion due to its inertia. To bring a moving object to a stop, an external force in the opposite direction of its motion needs to be applied. This force acts as a deceleration or braking force, counteracting the object's momentum and eventually bringing it to rest.

Example: Consider a bicycle in motion. To come to a stop, the rider needs to apply the brakes. The braking force applied by the brake pads creates a frictional force that opposes the forward motion of the bicycle. This force gradually reduces the speed of the bicycle until it comes to a complete stop.

Conclusion:
The requirement of force to start a stationary object and stop a moving object is essential due to the resistance offered by inertia. In both cases, an external force is necessary to overcome or counteract the object's inertia or momentum, respectively. Therefore, the correct answer is option 'A' - force is required to start a stationary object and to stop a moving object.