Question

Velocity is determined by measuring distance and time. If the % error in measuring distance is 2% and the % error in measuring time is 1%, what is the maximum % error in measuring velocity?

Answer 1

Given:

Velocity is determined by measuring distance and time. The % error in measuring distance is 2% and the % error in measuring time is 1%.

To find:

Maximum % error in measuring velocity.

Calculation:

Velocity is calculated from the ratio of distance and time. Now , if there is a small error (<6%) in measurement of distance and time then the maximum error in velocity can be written as:

$\sf{ \therefore \: \dfrac{\Delta v}{v} \% = \dfrac{\Delta d}{d} \% + \dfrac{\Delta t}{t} \%}$

$\sf{ = > \: \dfrac{\Delta v}{v} \% = 2 \% + 1 \%}$

$\sf{ = > \: \dfrac{\Delta v}{v} \% = 3 \%}$

So, the maximum relative error in measurement of Velocity will be 3%.

Important things to note:

• This process is applicable only when the individual errors is less than 6%.

• The errors can only be added.