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

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+4t^(2)-t^(2) in SI units. Find the velocity, acceleration, at t=2s, and the average velocity during 3rd second.
Answer» SOLUTION :`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.