Let v(t) be the velocity (in meters/second) of Alice’s race cart seconds after t
ID: 1612934 • Letter: L
Question
Let v(t) be the velocity (in meters/second) of Alice’s race cart seconds after the start of a race. Several measurements of v(t) are given in the chart below.
Assume that between each pair of consecutive values of t shown in the table, v(t) is either always strictly increasing or always strictly decreasing.
(a) Based on the data provided, find the best possible upper estimate of the distance Alice’s race car traveled during the first 50 seconds of the race.
(b) Based on the data provided, find the best possible lower estimate of the distance Alice’s race car traveled during the first 50 seconds of the race.
(c) Suppose we wanted to estimate the distance Alice’s race car traveled between 30 and 50 seconds after the start of the race to within 0.1 meters of the actual distance. How often must we take velocity measurements in order to be sure that we can determine this information?
Please explain all answers.
t 0 10 25 30 50 v(t) 0 30 40 35 45Explanation / Answer
The velocity is given by, V = distance /time = S/t
Following is the updated table including the distance calculated for each column.
(a) The best possible upper estimate of the distance Alice's race car travelled during first 50 seconds of the race
is 2250 m as shown in the last column
(b) The best possible lower estimate of the distance Alice's race car travelled during first 50 seconds of the race
is 300 m as shown in the second column column
(c) We wanted to estimate the distance Alice's race car travelled between 30 and 50 seconds.
The velocity is in the range of 35m/s to 45m/s
The distance travelled between 30 and 50 seconds is (2250 - 1050) = 1200 m
The estimate is required to within 0.1m of the actual distance.
At 30 s, estimated distance is (0.1)(1050) = 105m
Velocity at this estimated distance = v = s/t = 105/30 = 3.5 m/s
At 50 s, estimated distance is (0.1)(2250) = 225m
Velocity at this estimated distance = v = s/t = 225/50 = 7.5 m/s
Now we take the average of above two velocities.
vav = (3.5+7.5) / 2
vav =5.5 m/s. For better coverage on periodicity of measurements we can consider vav =5 m/s.
Therefore the velocity measurements can be taken at every 5m/s in increments.
t (seconds) 0 10 25 30 50 v(t) (m/s) 0 30 40 35 45 S (m) = v(t) * t 0 300 1000 1050 2250Related Questions
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