Applications Of Differential Calculus — Quiz 3

Questions in this quiz (7)

1. A particle starting at rest at $$t=0$$ moves along a line so that its acceleration at time $$t$$ is $$a(t)=10t$$. How much distance does the particle cover during the first $$4$$ seconds?

   • $$40$$ feet
   • $$106.7$$ feet
   • $$64$$ feet
   • $$80$$ feet

2. $$\int\frac{(3-y)^2}{2\sqrt{y}}dy=$$?

   • $$\frac{1}{3}(3-y)^3\sqrt{y}+C$$
   • $$3\sqrt{y}-2y^{3/2}+\frac{2}{5}y^{5/2}+C$$
   • $$9y^{1/2}-2y^{3/2}+\frac{1}{5}y^{5/2}+C$$
   • $$3y^{1/2}-2y^{3/2}+\frac{1}{5}y^{5/2}+C$$

3. $$\int e^{3\ln u}du=$$?

   • $$\frac{1}{3}u^3+C$$
   • $$\frac{u^3}{3u}+C$$
   • $$\frac{1}{4}u^4+C$$
   • $$u^3+C$$

4. $$\int\frac{\sin\theta}{1+\cos^2\theta}d\theta=$$?

   • $$\ln(1+\cos^2\theta)+C$$
   • $$-\tan^{-1}(\cos\theta)+C$$
   • $$\tan^{-1}(\cos\theta)+C$$
   • $$\frac{1}{1+\cos^2\theta}+C$$

5. $$\int\frac{dy}{y(2+\ln y^2)}=$$?

   • $$\ln|y|+\frac{1}{2}\ln|\ln y|+C$$
   • $$\frac{1}{2}\ln|2+\ln y^2|+C$$
   • $$\tan^{-1}(\ln|y|)+C$$
   • $$\frac{1}{(2+\ln y)^2}+C$$

6. Find the acceleration in $$ft/sec^2$$ needed to bring a particle moving with a velocity of $$60ft/sec$$ to a stop in $$4$$ seconds.

   • $$-5$$
   • $$-10$$
   • $$-15$$
   • $$-20$$

7. A particle moves along a line with acceleration $$a(t)=4+2t$$ at time $$t$$. When $$t=0$$, its velocity equals $$2$$ and it is at position $$s=1$$. When $$t=2$$, its position $$s=$$?

   • $$9$$
   • $$11$$
   • $$13.5$$
   • $$15.7$$