What is the numerical ratio of average velocity to average speed of an...
Numerical Ratio of Average Velocity to Average Speed of an Object Moving Along a Straight Line
Introduction
When an object moves along a straight line, it has a certain average speed and average velocity. The average speed of an object is the total distance traveled divided by the time taken to travel that distance, while the average velocity is the displacement divided by the time taken.
Formulae
The formulae for average speed and average velocity are as follows:
Average Speed = Total Distance / Time Taken
Average Velocity = Displacement / Time Taken
Numerical Ratio
The numerical ratio of average velocity to average speed of an object moving along a straight line can be calculated by dividing the average velocity by the average speed.
Mathematically, the ratio can be expressed as:
Average Velocity / Average Speed = (Displacement / Time Taken) / (Total Distance / Time Taken)
Simplifying the above expression, we get:
Average Velocity / Average Speed = Displacement / Total Distance
Thus, the numerical ratio of average velocity to average speed of an object moving along a straight line is equal to the displacement divided by the total distance traveled.
Explanation
The average speed of an object is the rate at which it covers distance, while the average velocity is the rate at which it changes its position. In the case of an object moving along a straight line, the distance traveled and the displacement are the same if the object moves in one direction only.
However, if the object changes its direction, then the displacement will be less than the total distance traveled. In this case, the numerical ratio of average velocity to average speed will be less than one, indicating that the object is not moving at a constant velocity.
Conclusion
The numerical ratio of average velocity to average speed of an object moving along a straight line is equal to the displacement divided by the total distance traveled. This ratio is an important concept in understanding the motion of objects and can be used to determine if an object is moving at a constant velocity or not.