### Home > APCALC > Chapter 11 > Lesson 11.3.2 > Problem11-94

11-94.

No calculator! A particle moves in the plane so that at any time $t$, $0 ≤ t ≤ 1$, its position is given by $x(t) =\frac { 1 } { 4 }e^{8t} − 2t$ and $y(t) = e^{4t}$. What are its velocity and speed when $t =\frac { 1 } { 4 }$?

$\$

$\vec{v}(t)=\langle x^\prime(t),y^\prime(t)\rangle$

$\text{speed}=\sqrt{(x^\prime(t))^2+(y^\prime(t))^2}$