By using a 2-meter stick (like the one in lab) marked in millimeters and a stopwatch that measures to 1/100h of a second, you decide to measure the speed of a motorized toy car that travels at a constant velocity. You measure out a 162.0cm interval with the 2-meter stick and time how long it takes the car to travel that distance using the stopwatch. Repeating the ex 2.95 s Calculate the average speed of the toy car What are the absolute and relative uncertainties of the distance and time measurements? Which measurement is more uncertain? Use the weakest link rule to determine the relative and absolute uncertainty in your speed estimation. Explain why it is necessary to calculate relative uncertainties. Why is absolute uncertainty not enougn ent 5 times you get the following time dа ta: 3.11 s 3.15 s 2.84 s 2.97 s

The average speed of a body is defined as the ratio between total distance and total time

v = dx / dt

v = 162.0 / 2.95

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

Δx = 0.1 cm

Δt = 0.01 s

Relative errors (uncertainties) are the absolute errors between the measured value

Er = Δx / x

Er = 0.1 / 162.0

Er = 6.2 10⁻⁴ length

Er = 0.01 / 2.95

Er = 3.4 10⁻³ time

The most uncertain measure is the time to have a greater relative error

Let's calculate the relative speed error

Δv / v = dv / dx dx + dv / dt dt

dv / dx = 1 / t

dv / dt = x (-1 / t²)

Er = Δv / v = 1 / t Δx + x / t² Δt

Er = 0.1 / 2.95 + 162.0/2.95² 0.01

Er = 0.034 + 0.19

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

Er = Δv / v

Δv = Er v

Δv = 0.22 54.9

Δv = 12 cm / s

v± Δv = (5 ±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