GATE 2015 CS (CS3) – Question 36
A motorbike starts from rest. Its velocity v in km/min at times t in minutes is:
| t | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|
| v | 10 | 18 | 25 | 29 | 32 | 20 | 11 | 5 | 2 | 0 |
Use Simpson’s one-third rule to estimate distance in 20 minutes, rounded to two decimal places.
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Show answer and explanation
Correct answer: 308 to 310
Explanation
Include the initial sample v(0)=0 because the bike starts from rest. With step h=2, odd-index velocities sum to 10+25+32+11+2=80; interior even-index velocities sum to 18+29+20+5=72. Simpson’s estimate is (2/3)[0+0+4×80+2×72]=928/3≈309.33 km, within the published 308–310 interval.