Given: a. find the value of t in the open interval...

given:
a. find the value of t in the open interval (0,2) for whichthe line tangent at (t,f(t)i sparallel to the line through (0,0)and (2,4p)
b. suppose the given funciton describes the position of aparticle on the x-axis for time 0?t?2.
what is the averrage celocity of the particle over thatinterval?
(c) derermine the celocity and the acceleration of theparticle at t=1
please if you know answer, can you explain detail forme?

Answers ( 1 )

  1. maélie perez
    maélie perez
    (a) Slope of the tangent is :
    The slope of the line joining (0,0) and (2,4p) is (4p-0)/(2-0)=2p
    Since the tangrnt line is parallel to given line thentheir slopes must be equal that is
       
    that is cos(2pt) =0 that is 2pt = p/2,3p/2,5p/2,7p/2,9p/2,..........
        that is t =1/4,3/4,5/4,7/4        (notethat t must be in interval(0,2))
    (b) Velocity of the particle is
    then average velocity for 0 £ t £ 2 is
    (c) Acceleration of the particle is
    velocity for t=1 is
    and acceleration for t=1 is    (as sin2p=0)

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