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Question

Difficulty: MediumMeasurement of Time

A stopwatch with a zero error of −0.25 s-0.25\text{ s} is used to record the time taken for an object to travel down an inclined path. If the stopwatch displays a time reading of 14.65 s14.65\text{ s} at the end of the motion, what is the true time elapsed in seconds?

Answer: 14.9 s

Answer

The true time elapsed is 14.90 seconds.
The correct answer is obtained by subtracting the zero error from the observed reading. Since the stopwatch has a negative zero error of −0.25 s-0.25\text{ s}, the true time is 14.65 s−(−0.25 s)=14.90 s14.65\text{ s} - (-0.25\text{ s}) = 14.90\text{ s}.

Step-by-Step Solution

1
Apply the zero error correction formula for measurement instruments
Actual Time = Displayed Time - Zero Error
Zero error represents a constant bias on the instrument that must be subtracted from the uncorrected reading.
2
Substitute the given values into the formula
Actual Time = 14.65 s - (-0.25 s)
The instrument starts behind zero by 0.25 s, so the zero error value is negative.
3
Perform the calculation
Actual Time = 14.90 s
Subtracting a negative quantity is mathematically equivalent to adding its positive magnitude.

Key Concept

Zero Error Correction in Stopwatch Time Measurement
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Topics

Measurement of Time

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