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If the velocity of a particle is v = A + Bt², where A and B are constants, then the distance travelled by it between 1s and 2s is:

1. 3/2 A + 7B
2. 3A + 7B
3. 3A + 4B
4. 3A + B/2

Correct answer: 3A + 7B

Solution

The distance travelled is obtained by integrating the velocity function v = A + Bt² with respect to time from t = 1s to t = 2s. The integral gives s = At + (Bt³)/3. Substituting the limits, the result is 3A + 7B.

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