ap-calculus-bc 1998 Q6

ap-calculus-bc · Usa · free-response Connected Rates of Change Parametric or Curve-Based Particle Motion Rates

A particle moves along the curve defined by the equation $y = x^{3} - 3x$. The $x$-coordinate of the particle, $x(t)$, satisfies the equation $\dfrac{dx}{dt} = \dfrac{1}{\sqrt{2t+1}}$, for $t \geq 0$ with initial condition $x(0) = -4$.
(a) Find $x(t)$ in terms of $t$.
(b) Find $\dfrac{dy}{dt}$ in terms of $t$.
(c) Find the location and speed of the particle at time $t = 4$.

A particle moves along the curve defined by the equation $y = x^{3} - 3x$. The $x$-coordinate of the particle, $x(t)$, satisfies the equation $\dfrac{dx}{dt} = \dfrac{1}{\sqrt{2t+1}}$, for $t \geq 0$ with initial condition $x(0) = -4$.\\
(a) Find $x(t)$ in terms of $t$.\\
(b) Find $\dfrac{dy}{dt}$ in terms of $t$.\\
(c) Find the location and speed of the particle at time $t = 4$.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6