A driver at Dewaan Motors is testing a new model car with a speedometer calibrated to read m/s rather than km/h. The following series of speedometer readings were obtained during a test run along a long, straight road: Time (s) 0 1 3 5 7 9 11 13 15 17 19 Speed (m/s) 0 0 4 7 10 13 17 22 23 26 29 (a) Compute the average acceleration during each 2-s interval. Is the acceleration constant? Is it constant during any part of the test run? (b) Make a (v-t) graph of the data, using scales of 1cm = 1s horizontally and 1cm = 2m/s vertically. Draw a smooth curve through the plotted points. By measuring the slope of your curve, find the instantaneous acceleration at t = 6 s, 18 s, and 25 s.
Answers
Given:
Time (s) : 0 1 3 5 7 9 11 13 15 17 19
Speed (m/s) : 0 0 4 7 10 13 17 22 23 26 29
To find:
(a) Compute the average acceleration during each 2-s interval. Is the acceleration constant? Is it constant during any part of the test run?
(b) Make a (v-t) graph of the data, using scales of 1cm = 1s horizontally and 1cm = 2m/s vertically. Draw a smooth curve through the plotted points. By measuring the slope of your curve, find the inst_antaneous acceleration at t = 6 s, 18 s, and 25 s.
Solution:
The average acceleration is given by
Using the above data calculate the acceleration for different intervals.
a₁ = (4 - 0) / (3 - 1) = 4 / 2 = 2m/s²
a₂ = (7 - 4) / (5 - 3) = 3 / 2 = 1.5m/s²
a₃ = (10 - 7) / (7 - 5) = 3 / 2 = 1.5m/s²
a₄ = (13 - 10) / (9 -7) = 3 / 2 = 1.5m/s²
a₅ = (17 - 13) / (11 - 9) = 4 / 2 = 2m/s²
a₆ = (22 - 17) / (13 - 11) = 5 / 2 = 2.5m/s²
a₇ = (23 - 22) / (15 - 13) = 1 / 2 = 0.5m/s²
a₈ = (26 - 23) / (17 - 15) = 3 / 2 = 1.5m/s²
a₉ = (29 - 26) / (19 - 17) = 3 / 2 = 1.5m/s²
The following table shows the result for each interval:-
Time (s) : 0 1 3 5 7 9 11 13 15 17 19
Speed (m/s) : 0 0 4 7 10 13 17 22 23 26 29
a : 2 1.5 1.5 1.5 2 2.5 0.5 1.5 1.5
The acceleration is constant from 5s to 9s.
