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 = 8.1 meters, Δx = 0.9 meters and t = 1.7 seconds and Δt = 1.7 seconds. What is the uncertainty in the average speed, Δv ?

Answer 1

Answer:

$\frac{\Delta v}{v}=0.426$

Step-by-step explanation:

you have that the average sped is given by the following formula:

$v(x,t)=\frac{x}{t}$

The uncertainty formula for a division is given by:

$\frac{\Delta v}{v}=\sqrt{(\frac{\Delta x}{x})^2+(\frac{\Delta t}{t})^2}$        (1)

Δv: uncertainty in speed

Δx: uncertainty in the distance = 0.9m

Δt: uncertainty in time = 0.7s

x: distance = 8.1m

t: time = 1.7s

You replace the values of all parameters in the equation (1):

$\frac{\Delta v}{v}=\sqrt{(\frac{0.9}{8.1})^2+(\frac{0.7}{1.7})^2}\\\\\frac{\Delta v}{v}=0.426$

Hence, the relation between the uncertainty in the average velocity is 0.426