A particle moves in a plane such that its velocity at time is v (t)=30 i +(40-10 t) j…

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

Problem

A particle moves in a plane such that its velocity at time

t

\mathbf{v}(t)=30 \hat{\mathbf{i}}+(40-10 t) \hat{\mathbf{j}}

and it passes through the origin at

t=0

. Find the expression for its position vector

\mathbf{r}(t)