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Question:

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

3A+7B

32A+73B

32A+4B

A²+B³

Solution:

We know that v = dS/dt
Integrating, S = ∫vdt = ∫₁² (At+Bt²)dt = A/2(2² - 1²) + B/3(2³ - 1³) = 32A + 73B