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.