Section II Part A — Full Practice Exam 1

Questions in this quiz (2)

1. The following formula gives the velocity of a particle moving along the $$x$$-axis at time $$t$$, where $$0\le t\le6$$:$$v(t)=2+4\sin(2t)-3\cos t.$$$$a.$$ At $$t=3$$ seconds, is the particle moving to the left or to the right?$$b.$$ From $$t=0$$ to $$t=6$$, what is the particle's average velocity?$$c.$$ From $$t=0$$ to $$t=6$$, what is the particle's average acceleration?$$d.$$ Determine $$p(2)$$, given that $$p(0)=5$$ and $$p(t)$$ represents the particle's position at time $$t$$.

   • right, $$ $$\frac{1}{6}\left(14-2\cos(12)-3\sin(6)\right)$$, $$\frac{3+4\sin(12)-3\cos(6)}{6}$$, $$p(2)=11-2\cos(4)-3\sin(2)$$
   • right, $$ $$\frac{1}{6}\left(14-2\cos(12)-3\sin(6)\right)$$, $$\frac{3+4\sin(12)-3\cos(6)}{6}$$, $$p(2)=11-2\cos(4)-3\sin(2)$$

2. The amount of a chemical in a container is proportional to the rate at which it decays. The relationship is modeled by $$\frac{dA}{dt}=-kA,$$ where $$A$$ is the amount of the chemical at time $$t$$. After $$10$$ hours, $$60$$ grams of the chemical remain, compared to the initial $$120$$ grams.$$a.$$ For time $$t$$, write an expression for $$A(t)$$, the amount of chemical remaining.$$b.$$ After $$5$$ hours, how much of the chemical has decayed?$$c.$$ Find the average amount of chemical in the container over the first $$20$$ hours.$$d.$$ How many hours will it take for the amount found in part $$c$$ to remain in the container?

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