Question

Find the uncertainty in a calculated average speed from the measurements of distance and time. Average speed depends on distance and time according to this function v(t,x) = x/t. Your measured distance and time have the following values and uncertainties x = 7.5 meters, delta x space equals space 1.4 meters and t = 2.9 seconds and delta t space equals space 1 seconds. What is the uncertainty in the average speed, delta v ?

Answer 1

Answer:

delta of velocity is 1.558 m/s

Step-by-step explanation:

The main problem is to determine degree of association with the rule of rounding and errors calculation. As out main equation includes division, the following rule can be applied:

$v+-ev=(x+-ex)/(t+-et)$ where ev- delta v, ex- delta x, et- delta t

As a result, we need to calculate the worst case scenarios: maximum distance over minimum time and minimal distance over the largest time to get maximum and minimum velocity:

$Vmax=Xmax/Tmin=(7.5+1.4)/(2.9-1)=8.9/1.9=4.68 m/s\\Vmin=Xmin/Tmax=(7.5-1.4)/(2.9+1)=6.1/3.9=1.564 m/s$

Then, we can calculate the value of velocity and its error:

$V=3.122+-1.558 m/s$

Note, that delta t was used as 1 s.