The displacement of a partical as a function of time t is given by `s=alpha+betat+gammat^(2)+deltat^(4)`, where `alpha`,`beta`,`gamma` and `delta` are constants. Find the ratio of the initial velocity to the initial acceleration.

Explanation

First find the velocity and acceleration in terms of time t, then use t=0 to find the intial values.
`s=alpha+betat+gammat^(2)+deltat^(4)`
`v=(ds)/(dt)=0+beta.1+gamma.2t+delta.4t^(3)`
`=beta+2gammat+4deltat^(3)`
`a=(dv)/(dt)=0+2gamma.1+4delta.3t^(2)`
`=2gamma+12deltat^(2)`
At `t=0, v=beta, a=2gamma`
`("Initial velocity")/("Initial acceleration")=beta/(2gamma)`