A particle moves along the x axis. The velocity of the particle at t is 6t-t^2 . what is the distance travelled by the object between t=0 and t=3?

1 Answer
Apr 12, 2018

See the answer below...

Explanation:

  • The velocity of the particle changes with the time as a relation #color(red)(v=6t-t^2#
  • Then, the displacement of the particle is,

#(ds)/(dt)=6t-t^2#

#=>ds=(6t-t^2)dt#

#=>s=int_0^3ds=int_0^3(6t-t^2)dt=[3t^2-t^3/3]_0^3#

#=>s=3xx3^2-3^3/3=18#

The displacement of the object is #18"unit"#

Hope it helps..
Thank you...

:-)