If `a=(3t^2+2t+1)` `m/s^2` is the expression according to which the acceleration of a particle varies. Then-
`a=(3t^2+2t+1)` `(m)/(s^2)`
Q. Find displacement of the particle after 2 seconds of start.

Options

A. 26 m
B. `(26)/(3)`m
C. `(30)/(7)`m
D. `(26)/(7)`m

Answer

B

Explanation

`int_(0)^(s)dS=int_(0)^(2)(t^(3)-t^(2)+t)dt`
`S=[(t^(4))/(4)+(t^(3))/(3)+(t^(2))/(2)]_(0)^(2)`
`S=4+(8)/(3)+2`
`S=(12+8+6)/(3)=(26)/(3)`