FORCE

There are numerous teachers of science who define force as a push or a pull. This is a very poor definition. The definition of force is embedded in Newton's first law of motion.

Newton's first law of motion may be stated as - Every body continues in its state of rest or of uniform motion in a straight line unless it is acted upon by an unbalanced force.

It is important to emphasise that all motion is relative. Having asked a student if she is sitting still I then ask her how many times she has been around the sun. Primary and secondary students readily pick up the concept of relative motion and frames of reference.

Uniform motion in a straight line means travelling in a straight line at a constant speed. Hence the velocity of the body is constant and therefore the acceleration is zero (a = dv/dt).

From Newton's first law an unbalanced force can do one of two things-

1. It can change a body's state of rest.

                                                       OR

2. It can change its state of uniform motion in a straight line.

Part 1 is quite straight forward. Suppose an object is at rest relative to a white board. If an unbalance force acts on the object it will now move relative to the white board.

Part 2 can be "quantized". Suppose the object is travelling in a straight line at a constant speed and an unbalanced force acts on it. Various outcomes are possible. The object-
(a). Continues moving in a straight line but changes its speed.
(b). Maintains the same speed but changes direction.
(c). Changes its speed and direction.

In all of the above cases the object changes its velocity with time and therefore must be accelerating.
It is to be noted that the definition of force is an operational definition. We do not say what a force is. Instead we say what a force can do. This concept is quite readily absorbed into the minds of attentive and motivated primary and secondary students.

ACCELERATION

There are numerous teachers of science who define acceleration as being the rate of change of speed with time. This is totally incorrect. With that definition we have acceleration = change in speed divided by change in time. Before looking at the true definition of acceleration I would like to mention distance,displacement, speed and velocity.

Suppose an objects initial position in three dimensional space is (0,0,0)m.Let an unbalanced force act on the object for 10 seconds. Suppose the object travels a distance of 200 metres and its final position is (100,0,0)m. Hence, distance travelled is 200m and the objects displacement is 100m. Its average speed is (change in distance) / (change in time) = 200/10 = 20m/s. Its average velocity = (change in displacement) / (change in time) = 100/10 = 10m/s.

Speed is a scalar quantity (it has magnitude only). Velocity is a vector quantity (it has magnitude and direction).

Acceleration is properly defined as being the rate of change of velocity with time. Acceleration is a vector quantity.

Suppose an object travels for 10s in a circular path at a constant speed of 15m/s. If acceleration was defined as (change in speed) / (change in time) then the acceleration of this object would be zero. This cannot be correct. An object travelling in a circle is being acted upon by an unbalanced force (otherwise it must be stationary or travelling in a staight line at constant speed according to Newton's First Law of Motion). If the inertial mass of the object is m and its mass remains constant then the force acting on the object = mass x acceleration. Hence, it must be accelerating. As it moves in a circle its velocity keeps changing with time. Hence, again it must be accelerating.