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 `3^(rd)` 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^2s)/(dt^2)=8-12t^2` when t=2
acc=`8-12xx2^2`=-40
acc=`-40 m//s^2`
displacement in 2 seconds
`s_1=6+4.2^2-2^4=6` m
displacement in 3 seconds
`s_2=6+4.3^2-3^4`=-39 m
displacement during `3^(rd)` second
`=s_2-s_1=-39-6=-45` m
`therefore` Average velocity during `3^(rd)` second
`=(pm 45)/1=-45` m/s
-ve sign indicates that the body is moving in opposite direction to the initial direction of motion.