Question

What is the relationship between acceleration and speed ?

Answer 1

Hint: Speed describes the change of an object’s position with respect to time. Is it the answer to the question how fast an object is moving? Whereas acceleration represents the change in velocity of an object. Even when an object is moving it can have zero acceleration if its velocity is constant.

Complete answer:
We know that speed, velocity and acceleration are all terms describing the motion of an object. First let us understand the meanings of these terms to find their relationships. Speed and velocity both tell you how fast an object is but there is a slight difference between them. We have to understand that speed is a scalar quantity, which means that it is only concerned about the distance travelled by the object in one second. Whereas velocity is a vector quantity, which is the distance travelled by the object and the direction in which it moves that second.

So, speed at an instant can be considered as the magnitude of the velocity vector at that time. Now, velocity has an upper hand in describing the motion of an object. In case of an object rotating around its axis, the object only changes its direction of motion rather than its position. So, the definition of speed is inadequate in this situation.

As we are a velocity is a vector quantity it can represent the change in direction as well and describe rotational motion as change in direction.Now, acceleration is to describe the change in velocity of a body. That is, it is the rate of change of the velocity, or in other terms it is the derivative of the velocity vector. It is also a vector quantity.

So, speed is the magnitude of velocity vector while acceleration is the derivative of the velocity vector.

Note: Having zero acceleration does not mean that the object is immobile. It implies that the object is moving with constant velocity. Also, an object will have velocity if it is only changing its direction continuously, but its speed will be zero.