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 was 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.
Answer this question plz
To calculate the average acceleration during each 2-second interval, we need to find the change in velocity and divide it by the time interval. The formula for average acceleration is:
Average acceleration = (change in velocity) / (time interval)
Let's calculate the average acceleration for each 2-second interval:
Time interval 1: (0-0)/(1-0) = 0 m/s²
Time interval 2: (4-0)/(3-1) = 2 m/s²
Time interval 3: (7-4)/(5-3) = 1.5 m/s²
Time interval 4: (10-7)/(7-5) = 1.5 m/s²
Time interval 5: (13-10)/(9-7) = 1.5 m/s²
Time interval 6: (17-13)/(11-9) = 2 m/s²
Time interval 7: (22-17)/(13-11) = 2.5 m/s²
Time interval 8: (23-22)/(15-13) = 0.5 m/s²
Time interval 9: (26-23)/(17-15) = 1.5 m/s²
Time interval 10: (29-26)/(19-17) = 1.5 m/s²
To determine if the acceleration is constant, we need to check if the average acceleration remains the same for each 2-second interval. From the calculations above, we can see that the average acceleration is not constant. It varies between 0 and 2.5 m/s².
To make a (v-t) graph, we plot the time (t) on the x-axis and the velocity (v) on the y-axis. We use a scale of 1 cm = 1 s horizontally and 1 cm = 2 m/s vertically.
Plotting the given data points on the graph:
(0, 0)
(1, 0)
(3, 4)
(5, 7)
(7, 10)
(9, 13)
(11, 17)
(13, 22)
(15, 23)
(17, 26)
(19, 29)
Drawing a smooth curve through these points, we get our (v-t) graph.
To find the instantaneous acceleration at specific times (t = 6 s, 18 s, and 25 s) from the graph, we measure the slope of the curve at these points. The slope of a curve represents the instantaneous acceleration.
Thus, we can measure the slope at t = 6 s, 18 s, and 25 s using a ruler or a protractor and then convert it to the corresponding acceleration values using the scale provided (1 cm = 2 m/s).