Velocity-time equation of a particle moving in a straight line is, `v=(10+2t+3t^2)` (SI units) Find
(a) displacement of particle from the mean position at time `t=1s,` if it is given that displacement is 20m at time `t=0`.
(b) acceleration-time equation.

Explanation

(i) The given euation can be written as,
`v=(ds)/(dt)=(10+2t+3t^(2))`
or `ds = (10+2t+3t^(2))dt`
or `int_(20)^(s)ds= int_(0)^(1)(10+2t+3t^(2))dt`
or `s=20 = [10t+t^(2)+t^(3)]_(0)^(1)`
or `s=20+12=32 m`
(ii) Acceleration - time equation can be obtained by differentiating the given equaiton w.r,t, time, Thus,
`a=(dv)/(dt)=(d)/(dt)(10+2t+3t^(2)) or `a=2+6t`