The motion of a particle along a straight line is described by the function `s=6+4t^(2)-t^(4)`
in SI units.Find the velocity ,acceleration ,at t=2s,and the average velocity during 3rd second.

Explanation

`s=6+4t^(2)-t^(4)`
velocity=`(ds)/(dt)=8t-4t^(3)` when t=2
velocity`=8xx2-4xx2^(3)` velocity =-16 m/s
Acceleration `a=(d^(2)S)/(dt^(2))=8 " " 12t^(2)` when t-2
acc =8-`12xx2^(2)`=-40 acc= `-40 m//s^(2)`
displacement in 2 second `s_(1)=6+4.2^(2)-2^(4)=6m`
displacement in 3 seconds `s_(2)=64.3^(2)-3^(4)=-39m`
Displacement during `3^(rd)` second
`=s_(2)-s_(1)=-39-6=-45m`
`therefore` Average velocity during `3^(rd)` second `(pm45)/(1)=-45 m/s`
-ve sign indicates that the body is moving in opposite direction to the initial direction of motion.