A runner is filmed with a high-speed camera as she travels in the positive x-direction along a straight track. Successive images are recorded every 0.30 s, and the measured displacements between adjacent images are listed below.
0–0.30 s: 0.60 m
0.30–0.60 s: 0.70 m
0.60–0.90 s: 0.90 m
0.90–1.20 s: 1.10 m
1.20–1.50 s: 1.20 m
1.50–1.80 s: 1.20 m
1.80–2.10 s: 1.10 m
2.10–2.40 s: 0.90 m
2.40–2.70 s: 0.70 m
2.70–3.00 s: 0.60 m
Assume the runner moves only in the +x direction throughout the 3.00 s interval.
(a) Describe qualitatively how the runner’s speed changes during the 3.00 s. Refer to specific intervals from the data table in your description.
(b) Using the numerical data, plot the runner’s speed versus time for the 10 equal-duration intervals. Connect the data points with a smooth curve that reflects the trend suggested by the data.
(c) From your speed–time graph, estimate the magnitude of the runner’s greatest instantaneous acceleration. Clearly indicate on the graph where this acceleration occurs and show how you obtained its value.
(d) Sketch a qualitative acceleration–time graph for the entire 3.00 s interval. Indicate the sign of the acceleration at all times and label when it is zero.
(e) Explain how the shape of your acceleration–time graph accounts for the approximate symmetry evident in the motion diagram data.