Barrons AP Calculus

(E) The velocity    v   of  the car is  linear  since   its acceleration    is  constant:

(D)

(A) a   =   v′(t)   =   1,1 for all t.

(B)

(B) Since   R   =   x,  y,  its slope   is   ;  since   v   =       its slope   is  .

If  R   is  perpendicular   to  v,  then        so

Since   (4, 3)  is  on  the curve,  the equation    must    be

x^2 + y     2   =   25.

(D) (t) =   t   2    + c 1 ,et + c 2 ;  since    (0)    =   2,0,    0^2 + c 1   =   2   and e^0 + c 2   =   0;

hence   c 1     =   2   and c 2     =   −1.

(B) The object’s    position    is  given   by      Since   the

object  was at  the origin  at      and 4   ·   1    + c 2  =   0,  making