Question

The acceleration a of a particle starting from rest varies with time according to relation, `a=alphat+beta`. Find the velocity of the particle at time instant t.
Strategy : `a=(dv)/(dt)`

Answer 1

Given that, `a=alphat+beta`
`(dv)/(dt)=alphat+beta`
`int_(0)^(v)dv=int_(0)^(t)(alphat+beta)dt=int_(0)^(t)alphatdt+int_(0)^(t)betadt`
`(v)_(0)^(v)=alpha int_(0)^(t)tdt+beta int_(0)^(t)dt`
`=alpha((t^(2))/(2))_(0)^(t)+beta(t)_(0)^(t)`
`v=(alpha)/(2)t^(2)+betat`