Question

Give Reasons for the following:
If the reading on the odometer of a vehicle in the beginning of a trip and after $$40$$ minutes were $$1048km$$ and $$1096km$$ respectively, will the reading on the speedometer show this velocity where the vehicle is moving? Support your answer with reason.

Answer 1

Odometer is used to measure the distance traveled by the vehicle
Given:
Initial Reading$$=1048km$$ at $$t=0$$ seconds
Final Reading $$=1096km$$ at $$t=40$$ minutes$$=\cfrac{40}{60}hr$$
$$Average\quad speed=\cfrac { Total\quad Distance\quad Covered }{ Total\quad Time\quad Taken } =\cfrac { 1096-1048 }{ 40/60 } =\cfrac { 48 }{ 40/60 } =72km\quad { hr }^{ -1 }$$
Calculations using the readings of odometer gives the average speed
Whereas, the speedometer gives the reading of instantaneous speed.
Thus, the two values, that is one calculated and one on the speedometer may not be the same
Both can only be the same if the vehicle has been moving with constant velocity throughout the measurement.