ap-calculus-ab 2006 Q2

ap-calculus-ab · USA · free-response_formB Variable acceleration (1D) Multi-part particle motion analysis (formula-based velocity)
A particle moves along the $x$-axis so that its velocity at any time $t \geqq 0$ is given by $v ( t ) = 1 - \sin ( 2 \pi t )$. (a) Find the acceleration $a ( t )$ of the particle at any time $t$. (b) Find all values of $t , 0 \leqq t \leqq 2$, for which the particle is at rest. (c) Find the position $x ( t )$ of the particle at any time $t$ if $x ( 0 ) = 0$.
: \text { integrand } 
A particle moves along the $x$-axis so that its velocity at any time $t \geqq 0$ is given by $v ( t ) = 1 - \sin ( 2 \pi t )$.
(a) Find the acceleration $a ( t )$ of the particle at any time $t$.
(b) Find all values of $t , 0 \leqq t \leqq 2$, for which the particle is at rest.
(c) Find the position $x ( t )$ of the particle at any time $t$ if $x ( 0 ) = 0$.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6