The velocity (v) of a tractor, which starts from rest, is given at fixed intervals of time (t) as follows. Using Simpson's 1/3rd rule, the distance covered by the tractor in 20 minutes will be _________ m.
Reproduction of the data table given with AG Q.30.
Official Answer Key:
25.80 to 25.90
Step-by-Step Solution & Explanation
h = 2 min, n = 10 intervals (even) — Simpson's 1/3 rule applies.
S = h/3 [ (y₀ + y₁₀) + 4(y₁ + y₃ + y₅ + y₇ + y₉) + 2(y₂ + y₄ + y₆ + y₈) ]
Odd-index sum = 0.8 + 2.1 + 2.7 + 0.9 + 0.2 = 6.7 ⇒ 4 × 6.7 = 26.8
Even-interior sum = 1.5 + 2.4 + 1.7 + 0.4 = 6.0 ⇒ 2 × 6.0 = 12.0
End ordinates = 0 + 0 = 0
S = (2/3)(0 + 26.8 + 12.0) = (2/3)(38.8) = 25.87 m — within the official range 25.80–25.90.
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