The position of a particle is given byr=3.0thati+2.0t^(2)hatj+5,0hatkwhere t is in seconds and the coefficients have the proper units for r to be in matres. (a) Find v (t) and a(t) of the particle . (b) Findthe magnitude and direction of v (t) at t=1.0 s.

The position of a particle is given byr=3.0thati+2.0t^(2)hatj+5,0hatkw

1.	The position of a particle is given byr=3.0thati+2.0t^(2)hatj+5,0hatkwhere t is in seconds and the coefficients have the proper units for r to be in matres. (a) Find v (t) and a(t) of the particle . (b) Findthe magnitude and direction of v (t) at t=1.0 s.
Answer» Solution :`V(t)=(DR)/(dt)=(d)/(dt)(3.0thati+2.0t^(2)hatj+5.0hatk)` `=3.0hati+4.0thatj` a `(t)=(dv)/(dt)=+4.0hatj` `a=4.0 "m s"^(-2)` along y- direction At t=1.0s, `v=3.0hati+4.0hatj` It .s magnitude is `v=sqrt(3^(2)+4^(2))=5.0 " m s"^(-1)`and direction is `theta=tan^(-1)((v_(y))/(v_(X)))=tan^(-1)((4)/(3))~=53^(@)`with x - axis.