A particle is moving rectilineraly so that its acceleration is given as `a = 3t^(2) + 1 m//s^(2)`. Its initial velocity is zero.

Options

A. The velocity of the particle at `t = 1` sec will be `2m//s`
B. The displacement of the particle in `1` sec will be `2m`.
C. The particle will continoue to move in positive direction.
D. The particle come back to its starting point after some time.

Answer

A, C

Explanation

`a = 3t^(2) + 1`
`(dV)/(dt) = 3 t^(2) + 1 rArr overset(v)underset(0)(int)dv = overset(t)underset(0)(int)(3t^(2) + 1)dt`
`v = (t^(3) + t)_(0)^(1) = 2 m//s. rArr v = t^(3) + t`
`:. overset(s)underset(0)(int)ds = overset(1)underset(0)(int)(t^(3) + 1)dt rArr S = (1)/(4) + (1)/(2) = 0.75`