Question

The relationship between average speed, time and distance is
(A) \[\text{Average speed = distance}\times \text{time}\]
(B) \[\text{Average speed = }\dfrac{\text{total distance}}{\text{total time}}\]
(C) \[\text{Time = average speed/distance}\]
(D) \[\text{Distance = average speed }\times \text{ time}\]

Answer 1

Hint: In everyday life, when an object is in motion, there are several factors at play. The moving body does not always maintain a constant speed. There might be instances when the body accelerates and instances when brakes are applied to cause deceleration. These irregularities in the practical motion move for a need of average speed.

Complete step by step answer:
As stated above, the irregularities in motion ask for uniformity to be present. In making calculations and analysis of motion, we need constant hard data, not an irregular plot of values. Hence average speed or the uniform speed is said to be that constant speed which has the same effect at the end of the motion as the actual irregular motion has.
If a body travels a certain distance in a given time where the speed of the body varies with time, the average speed would be the constant speed with which, if the body had travelled during its duration of motion, it would have covered the same distance.
The above statement can be a mouthful to read and to speak as well. When mathematically expressed, the average speed is very simple.
\[\text{Average speed = }\dfrac{\text{total distance}}{\text{total time}}\]
Hence option (B) is the correct answer.

Note: The above solution is the same as in the case of calculating averages for a given class of data, wherein we add the individual data to find the total sum and then divide it by the number of observations to find the average of the data. We have added the distance covered in small intervals of time, found their sum to find the total distance and then divided it by the total time to get the average speed.