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