Applications Of Differential Calculus — Quiz 3
Practice Applications Of Differential Calculus — Quiz 3 on The School of Mathematics (Applications Of Differential Calculus) with 7 scored questions. This set covers problems such as: “A particle starting at rest at t=0 moves along a line so that its acceleration at time t is a(t)=10t . How …”; “\int\frac{(3-y)^2}{2\sqrt{y}}dy= ?”; “\int\frac{\sin\theta}{1+\cos^2\theta}d\theta= ?”. Work carefully, check explanations for misses, then retake to track improvement before test day.
Questions in this quiz (7)
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
$$\int\frac{(3-y)^2}{2\sqrt{y}}dy=$$?
- $$\frac{1}{3}(3-y)^3\sqrt{y}+C$$
- $$3\sqrt{y}-2y^{3/2}+\frac{2}{5}y^{5/2}+C$$
- $$9y^{1/2}-2y^{3/2}+\frac{1}{5}y^{5/2}+C$$
- $$3y^{1/2}-2y^{3/2}+\frac{1}{5}y^{5/2}+C$$
$$\int e^{3\ln u}du=$$?
- $$\frac{1}{3}u^3+C$$
- $$\frac{u^3}{3u}+C$$
- $$\frac{1}{4}u^4+C$$
- $$u^3+C$$
$$\int\frac{\sin\theta}{1+\cos^2\theta}d\theta=$$?
- $$\ln(1+\cos^2\theta)+C$$
- $$-\tan^{-1}(\cos\theta)+C$$
- $$\tan^{-1}(\cos\theta)+C$$
- $$\frac{1}{1+\cos^2\theta}+C$$
$$\int\frac{dy}{y(2+\ln y^2)}=$$?
- $$\ln|y|+\frac{1}{2}\ln|\ln y|+C$$
- $$\frac{1}{2}\ln|2+\ln y^2|+C$$
- $$\tan^{-1}(\ln|y|)+C$$
- $$\frac{1}{(2+\ln y)^2}+C$$
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.
- $$-5$$
- $$-10$$
- $$-15$$
- $$-20$$
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 $$s=$$?
- $$9$$
- $$11$$
- $$13.5$$
- $$15.7$$