Question

Can a body have a constant speed and still have a varying velocity?

Answer 1

The application of the concept of variable velocity and at what conditions the body may vary with velocity needs to be probed upon. The difference between the concepts of speed and velocity must be determined in order to know whether a body can have differing values of speed and velocity. The problem requires the need to consider examples where the body may possess varying velocity with a constant speed and also differentiate between the different types of velocities and speeds.

Complete answer:
In order to know whether a body will exhibit varying velocity with a constant speed we first need to know the concepts of speed and velocity. The speed is defined to be the total distance travelled by the object divided by the total time taken to cover that distance. The velocity of the particle is said to be the ratio of the total displacement of the particle by the time interval in which the displacement occurs.

However, for the above question there is a requirement to deal with variable velocity. The quantity of velocity can be of four different types, namely, average velocity, variable velocity, instantaneous velocity and uniform velocity. These three types of velocities differ slightly with each other.

By definition, an object is said to be moving with variable velocity when either its speed changes or its direction of motion changes or both change along with time. As its name suggests the body’s velocity changes continuously with time.

Now, let us see when the body may have a constant speed. Constant speed refers to an object moving at a steady rate which means that its instantaneous value of speed will remain unchanged throughout its travel. Instantaneous speed is the speed of the object at a particular instant of time or at a particular point in its path.

We now need to determine an example when the body will exhibit motion which has a variable velocity but a constant speed in order to prove that it is possible for a body to possess a constant speed with a varying velocity.

A body moving in a uniform circular motion is said to have a variable velocity at all points of the circular path and a constant speed throughout. Speed is known to be a scalar quantity and hence it is only associated with a magnitude which must remain constant as per our question.

Knowing this, we can say that the magnitude of speed is given by the total distance that the body covers in a particular time interval and when a body is moving in a circular motion the distance that needs to be covered does not vary and hence the speed at every instant of the path remains unchanged.

Since velocity is a vector quantity they are said to contain both magnitude and direction. The direction associated with the motion of the body in a uniform circle is said to vary at every moment and this can be determined by drawing tangents to the circle at each point in the circle which will be different. Since there is a variation in the direction of motion even though the speed remains constant, a body in uniform circular motion is said to have variable velocity, as per the definition of variable velocity mentioned above.

Note: Even though it can be seen in the above solution of the problem that a body can have a constant speed but still a varying velocity the opposite cannot happen. This means that it cannot have a constant velocity with a variable speed. The two quantities, namely, speed and velocity are two differing concepts and are often mistaken to be the same. Speed depends on the distance covered and velocity depends on the displacement which also seem to be two different quantities.