For a particle moving along a straight line, the displacement x depends on time t as `x = alpha t^(3) +beta t^(2) +gamma t +delta`. The ratio of its initial acceleration to its initial velocity depends

Options

A. only on `alpha` and `gamma`
B. only on `beta` and `gamma`
C. only on `alpha` and `beta`
D. only on `alpha`

Answer

B

Explanation

`upsilon=3alpha t^(2)+2beta t+gamma : upsilon_(t=0)=upsilon_(i)=gamma`
`a=6alpha t+2beta: a_(t=0)=a_(i)=2beta`
`therefore (upsilon_(i))/(a_(i))=(gamma)/(2beta)`