Velocity and Speed

Before understanding the numerical ratio of velocity to speed, let's understand the basic difference between velocity and speed:

- Velocity is a vector quantity that describes the rate of change of an object's position with respect to time and in a particular direction. Velocity is given by the formula v = Δs/Δt, where v is the velocity, Δs is the change in position, and Δt is the change in time.
- Speed is a scalar quantity that describes how fast an object is moving without any regard to direction. Speed is given by the formula s = d/t, where s is the speed, d is the distance traveled, and t is the time taken.

Numerical Ratio of Velocity to Speed

The numerical ratio of velocity to speed is given by the formula v/s. Now, let's analyze the options given in the question:

a) Either less than or equal to 1: This option is correct because the magnitude of velocity can be less than, equal to, or greater than speed. However, the direction of velocity must be taken into account while comparing it with speed. Since velocity has both magnitude and direction, it can be negative, positive, or zero. Hence, the numerical ratio of velocity to speed can be less than or equal to 1.

b) Equal to 1: This option is incorrect because the magnitude of velocity can be greater than speed. In such cases, the numerical ratio of velocity to speed will be greater than 1.

c) Greater than 1: This option is incorrect because the numerical ratio of velocity to speed can be less than or equal to 1 as explained above.

d) Less than 1: This option is incorrect because the numerical ratio of velocity to speed can be greater than or equal to 1 as explained above.

Conclusion

Hence, we can conclude that option 'A' is the correct answer, as the numerical ratio of velocity to speed can be either less than or equal to 1.