This can be done using the step function of the Matplotlib function:
import matplotlib.pyplot as plt
x = [0., 27.82, 40.12, 75.33, 172.77, 208.64, 253., 335.21, 351.16,
590.38, 779.37, 968.35, 1220.66, 1299.17, 1318.32, 1352.7]
v = [13., 15., 14., 14., 17., 18., 21., 20., 25., 22., 21., 22., 20.,
19., 14., 9.]
plt.step(x, v, where='post')
plt.xlabel('Position [m]')
plt.ylabel('Speed [m/s]')
plt.show()
Result:

See this example for the difference between the different values โโof the 'where' argument. From your description, it seems that you want the "post" option.