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.

The motion of a particle along a straight line is described by the fun

1.	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.
Answer» Solution :`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.