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

Explanation

`s=6+4t^(2)-t^(4)`
Velocity `=(ds)/(dt)=8t-4t^(3)" when "t=2`
Velocity `=8xx2-4xx2^(3)`
Velocity `=-16m//s`
Acceleration `a=(d^(2)s)/(dt^(2))=8-12t^(2)" when "t=2`
acc `=8-12xx2^(2)=-40`
acc `=-40m//s^(2)`
displacement in 2 seconds
`s_(1)=6+4.2^(2)-2^(4)=6m`
displacement in 3 seconds
`s_(2)=6+4.3^(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)=-45m//s`
`-ve` sign indicates that the body is moving in opposite direction to the initial direction of motion.