Question
A formula connecting speed (s), distance (d) and time (t) is s=(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.
Answer
4.5
(309 Votes)
Ula
Expert · Tutor for 3 years
Answer
After performing the calculations, we find that the lower bound of speed is 24.2 (to 3 significant figures) and the upper bound of speed is 22.7 (to 3 significant figures).
Explanation
## Step 1: Understanding the ProblemThe problem requires us to calculate the lower and upper bounds of speed (s) given the distance (d) and time (t) to 2 significant figures. The formula connecting these three quantities is
.## Step 2: Calculating the BoundsTo calculate the bounds, we need to understand that the lower bound of a quantity is the smallest possible value it could be, and the upper bound is the largest possible value it could be. Given that the distance and time are provided to 2 significant figures, the lower bound of distance (d) would be 185 and the upper bound would be 195. Similarly, the lower bound of time (t) would be 8.05 and the upper bound would be 8.15.## Step 3: Calculating the Lower Bound of SpeedThe lower bound of speed (s) can be calculated by dividing the upper bound of distance by the lower bound of time. This is because to get the smallest possible value of speed, we need to divide the largest possible value of distance by the smallest possible value of time.###
## Step 4: Calculating the Upper Bound of SpeedSimilarly, the upper bound of speed (s) can be calculated by dividing the lower bound of distance by the upper bound of time. This is because to get the largest possible value of speed, we need to divide the smallest possible value of distance by the largest possible value of time.###