Respuesta :
Answer:
Explanation:
The average speed of a body is defined as the ratio between total distance and total time
Ā Ā v = dx / dt
Ā Ā v = 162.0 / 2.95
Ā Ā v = 54.9 m / s
The absolute errors (uncertainties) of the distance and time measurements as measured with instruments are the errors of the instruments
Ā Ā Ā Īx = 0.1 cm
Ā Ā Ā Īt = 0.01 s
Relative errors (uncertainties) are the absolute errors between the measured value
Ā Ā Ā Er = Īx /x
Ā Ā Ā Er = 0.1 / 162.0
Ā Ā Ā Er = 6.2 10ā»ā“ Ā Ā Ā Ā length
Ā Ā Ā Er = 0.01 / 2.95
Ā Ā Ā Er = 3.4 10ā»Ā³ Ā Ā Ā Ā time
The most uncertain measure is the time to have a greater relative error
Let's calculate the relative speed error
Ā Ā Ā Īv / v = dv / dx dx + dv / dt dt
Ā Ā Ā dv / dx = 1 / t
Ā Ā Ā dv / dt = x (-1 / tĀ²)
Ā Ā Ā Er = Īv / v = 1 / t Īx + x / tĀ² Īt
Ā Ā Ā Er = 0.1 / 2.95 + 162.0/2.95Ā² Ā 0.01
Ā Ā Ā Er = 0.034 + 0.19
Ā Ā Ā Er = 0.22
We can observe that the relative error of time is much higher than the relative error of distance, so to reduce the speed error, time must be measured with much more precision
Absolut mistake
Ā Ā Er = Īv / v
Ā Ā Īv = Er v
Ā Ā Īv = 0.22 54.9
Ā Ā Īv = 12 cm / s
Ā Ā vĀ± Īv = (5 Ā±1 ) 10 cm/s
When calculating the relative uncertainty, it is known which magnitude should be more precisely medical to reduce the total error of a derived magnitude
