ap-calculus-ab 2018 Q2

ap-calculus-ab · Usa · free-response Variable acceleration (vectors)
A particle moves along the $x$-axis with velocity given by $v ( t ) = \frac { 10 \sin \left( 0.4 t ^ { 2 } \right) } { t ^ { 2 } - t + 3 }$ for time $0 \leq t \leq 3.5$.
The particle is at position $x = - 5$ at time $t = 0$.
(a) Find the acceleration of the particle at time $t = 3$.
(b) Find the position of the particle at time $t = 3$.
(c) Evaluate $\int _ { 0 } ^ { 3.5 } v ( t ) \, dt$, and evaluate $\int _ { 0 } ^ { 3.5 } | v ( t ) | \, dt$. Interpret the meaning of each integral in the context of the problem.
(d) A second particle moves along the $x$-axis with position given by $x _ { 2 } ( t ) = t ^ { 2 } - t$ for $0 \leq t \leq 3.5$. At what time $t$ are the two particles moving with the same velocity? 
A particle moves along the $x$-axis with velocity given by $v ( t ) = \frac { 10 \sin \left( 0.4 t ^ { 2 } \right) } { t ^ { 2 } - t + 3 }$ for time $0 \leq t \leq 3.5$.

The particle is at position $x = - 5$ at time $t = 0$.

(a) Find the acceleration of the particle at time $t = 3$.

(b) Find the position of the particle at time $t = 3$.

(c) Evaluate $\int _ { 0 } ^ { 3.5 } v ( t ) \, dt$, and evaluate $\int _ { 0 } ^ { 3.5 } | v ( t ) | \, dt$. Interpret the meaning of each integral in the context of the problem.

(d) A second particle moves along the $x$-axis with position given by $x _ { 2 } ( t ) = t ^ { 2 } - t$ for $0 \leq t \leq 3.5$. At what time $t$ are the two particles moving with the same velocity?
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6