5.11.2. Exercise: Indexing/slicing/filtering unidimensional arrays 2#

The position of an object has been recorded in meters during one second at a sampling frequency of 100 Hz:

import numpy as np

p = np.array(
    [
        0.    , 0.0099, 0.0196, 0.0291, 0.0384, 0.0475, 0.0564, 0.0651,
        0.0736, 0.0819, 0.09  , 0.0979, 0.1056, 0.1131, 0.1204, 0.1275,
        0.1344, 0.1411, 0.1476, 0.1539, 0.16  , 0.1659, 0.1716, 0.1771,
        0.1824, 0.1875, 0.1924, 0.1971, 0.2016, 0.2059, 0.21  , 0.2139,
        0.2176, 0.2211, 0.2244, 0.2275, 0.2304, 0.2331, 0.2356, 0.2379,
        0.24  , 0.2419, 0.2436, 0.2451, 0.2464, 0.2475, 0.2484, 0.2491,
        0.2496, 0.2499, 0.25  , 0.2499, 0.2496, 0.2491, 0.2484, 0.2475,
        0.2464, 0.2451, 0.2436, 0.2419, 0.24  , 0.2379, 0.2356, 0.2331,
        0.2304, 0.2275, 0.2244, 0.2211, 0.2176, 0.2139, 0.21  , 0.2059,
        0.2016, 0.1971, 0.1924, 0.1875, 0.1824, 0.1771, 0.1716, 0.1659,
        0.16  , 0.1539, 0.1476, 0.1411, 0.1344, 0.1275, 0.1204, 0.1131,
        0.1056, 0.0979, 0.09  , 0.0819, 0.0736, 0.0651, 0.0564, 0.0475,
        0.0384, 0.0291, 0.0196, 0.0099
    ]
)

Knowing that:

\[ v(i) = \dfrac{p(i+1) - p(i-1)}{t(i+1) - t(i-1)} \]

Write a program of only 1 to 2 lines that calculates the speed of the object. Then, plot the velocity and position on a same figure to check your result.

Tip

Due to the calculation of speed that requires position values before and after the current sample, the velocity array will be 2 values shorter than the position array, as illustrated in Fig. 5.9.

Fig. 5.9 Calculating speed leads to a shorter array.#

Hide code cell content 
import numpy as np
import matplotlib.pyplot as plt

t = np.arange(100) / 100
v = (p[2:] - p[0:-2]) / (t[2:] - t[0:-2])

# Since the time step is regular at 0.01, we could also calculate v using a single line:
v = (p[2:] - p[0:-2]) / (2 * 0.01)

# Plot the result
plt.plot(t, p, label="Position (m)")
plt.plot(t[1:-1], v, label="Velocity (m/s)")
plt.xlabel("Time (s)")
plt.grid(True)
plt.legend()
plt.show()
_images/cdb58d604c51c9298101bb4852683080d88063cb2cab80164df0d3ab1283a428.png