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

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V = α t + β t 2 d s d t = α t + β t 2 ∫ S 1 S 2 d s = ∫ 1 2 α t + β t 2 d t S 2 - S 1 = α t 2 2 + β t 3 3 1 2 As the particle is not changing direction So distance = displacement. Distance = α [ 4 - 1 ] 2 + β [ 8 - 1 ] 3 = 3 α 2 + 7 β 3

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