Q2Advanced Engineering Mathematics I

Question

The distance covered by an athlete for the 50 meter race is given in the following table: | Time (Seconds) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---|---|---| | Distance (meters) | 0 | 2.5 | 8.5 | 15.5 | 24.5 | 36.5 | 50 | Determine the speed of the athlete at t = 5 sec.

Answer 1

Speed is the derivative of distance with respect to time ( $v = d x / d t$ ).

Since we need the speed at $t = 5$ , which is near the end of the table, we use Newton's Backward Difference Formula for derivatives.

Construct a backward difference table, find $\nabla y_{n}, \nabla^{2} y_{n}$ , etc., and substitute into the derivative formula.

Q2Advanced Engineering Mathematics I

Question

Answer