### Home > APCALC > Chapter 12 > Lesson 12.1.1 > Problem12-11

12-11.

A particle moves along the curve $y = \sin(x)$ at a constant speed of $5$ units per second. What is $x′(t)$, the $x$-component of the velocity vector, when $x = 2$

$5=\sqrt{(x^\prime(t))^2+(y^\prime(t))^2}\text{ or }25=(x^\prime(t))^2+(y^\prime(t))^2$

$\frac{dy}{dx}=\frac{y^\prime(t)}{x^\prime(t)}=\cos(x)$

$y^\prime(t)=x^\prime(t)\cos(x)$

$25=(x^\prime(t))^2+(x^\prime(t)\cos(x))^2)$

$x^\prime(t)=\sqrt{\frac{25}{1-\cos^2(x)}}$

Evaluate $x′(2)$.