The odometer of a car measures (and displays) the distance traveled by the vehicle, while the speedometer measures (and displays) the instantaneous speed of a vehicle. If the odometer of a car is not working, we can use the distance, speed and time relationship to calculate the distance traveled.

Distance traveled = speed x time

That is, distance traveled by a vehicle (the reading of odometer) is the product of speed of the vehicle and time taken. Since the speed of a vehicle is not constant, we have to integrate or add all the values of speed times the time.

So, if our odometer is not working, we can use a wall clock to determine the time we traveled at a particular speed and multiple the two. All such values (corresponding to each different) velocity will give us the total distance traveled. For example, if we found that we traveled at 20 m/s for 10 s, then changed the speed to 10 m/s and stayed at that speed for 10 s and finally were traveling at 5 m/s for 5 s; then the total distance traveled by us would be 20 x 10 + 10 x 10 + 5 x 5 = 200 + 100 + 25 = 325 m.

Hope this helps.

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