Question

Two vehicles travel along two distinct roads. The first vehicle traveled in the first roadway
with a spot speed equal to “A veh/hr”, while the second vehicle traveled along the second roadway
with a space mean speed equal to “A veh/hr”. If the two vehicles originated at the same position
and will arrive at the same points, who will arrive at the destination first? Elucidate, and
expound your idea based on the fundamental definitions and your logical reasoning.

Answer 1

Spot speed of a vehicle is defined as speed at a particular instant. Whereas sapce mean speed of vehicle is calculated as harmonic average of a number of spot speed readings. Harmonic average gives more weightage to the slower spot speed reading hence it is observed to be lesser than average time mean speed which is arthematic mean of spot speed readings. Space mean speed give more weightage to speed of slower vehicle but will always be higher than this. Therefore, if space mean speed of a vehicle X is equal to spot speed of another vehicle Y then it means that there will be more spot speeds values of vehicle X than spot speed value of vehicle Y. In other words, though space mean speed is weighted towards slow vehicle speed even then if the value of space mean speed of vehicle X is equal to spot speed of another vehicle Y then the spot speed values of the X vehicle is more than vehicle Y.

Therefore the vehicle Second with space mean speed equal to A which is equal to spot speed of First vehicle will be reaching fast at destination than that of First vehicle.