The velocity components of a particle are given by and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The velocity components of a particle are given by

\dfrac{dx}{dt}=t^{2}+1

and

\dfrac{dy}{dt}=3x

. The particle is at the point

(2,1)

when

t=0

. What is the value of

y

when

t=1

? (a)

\dfrac{29}{4}

(b)

\dfrac{35}{4}

(c)

\dfrac{31}{4}

(d)

\dfrac{28}{4}