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The instantaneous velocity of a particle moving in a straight line is given as v = αt + βt², where α and β are constants. The distance travelled by the particle between 1s and 2s is:

1. 3α + 7β
2. 3α/2 + 7β/3
3. α/2 + β/3
4. 3α/2 + 7β/2

Correct answer: α/2 + β/3

Solution

To find the distance traveled between 1s and 2s, we need to integrate the velocity function v = αt + βt² over that interval. The correct option, α/2 + β/3, results from evaluating the definite integral of the velocity function from t=1 to t=2, which gives the total distance traveled.

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