Under this assumption, during the first second, the object would move by {{MATH_179}}; during the second time interval of one second, the object would move by {{MATH_180}}, during the third second, the object would move by {{MATH_181}}, and during the last second, it would move by {{MATH_182}}. During the entire time interval, the object would move by {{ENV_183}} Using sigma notation and the fact that {{MATH_184}}, we can write {{MATH_185}} Again, we denote the sample points by {{MATH_186}}, {{MATH_187}}, and write {{MATH_188}} This is a left Riemann sum for the function {{MATH_189}} on the interval {{MATH_190}}, when {{MATH_191}}. This scenario is illustrated in the figure below. {{CMD_192}} {{ENV_193}} {{CMD_194}} Now, we approximate the displacement of the object assuming that the velocity is constant during half-second time intervals, and that velocity is equal to the velocity at the beginning of each time interval.