Problem

A formula connecting speed $(s)$, distance (d) and time $(t)$ is \[ s=\frac{d}{t} \] $d=190$ metres to 2 significant figures $t=8.1$ seconds to 2 significant figures Calculate the lower and upper bounds of $s$. Give your answers to 3 significant figures.

Solution

Step 1 :Given the distance $d=190$ metres to 2 significant figures and time $t=8.1$ seconds to 2 significant figures.

Step 2 :The formula connecting speed $(s)$, distance $(d)$ and time $(t)$ is $s=\frac{d}{t}$.

Step 3 :To find the lower and upper bounds of speed, we need to consider the lower and upper bounds of distance and time.

Step 4 :For distance, the lower bound is 185 and the upper bound is 195 (to 2 significant figures). For time, the lower bound is 8.05 and the upper bound is 8.15 (to 2 significant figures).

Step 5 :The lower bound of speed is found by dividing the upper bound of distance by the lower bound of time. So, $s_{lower} = \frac{d_{upper}}{t_{lower}} = \frac{195}{8.05} = 24.224$ m/s.

Step 6 :The upper bound of speed is found by dividing the lower bound of distance by the upper bound of time. So, $s_{upper} = \frac{d_{lower}}{t_{upper}} = \frac{185}{8.15} = 22.699$ m/s.

Step 7 :Final Answer: The lower bound of speed is \(\boxed{22.699}\) m/s and the upper bound of speed is \(\boxed{24.224}\) m/s.

From Solvely APP
Source: https://solvelyapp.com/problems/17153/

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