AP Calculus BC : 4.4 Introduction to Related Rates- Exam Style questions with Answer- MCQ

Question

Ohm’s law states that if the resistance of the path of current between two points is constant, then the voltage difference V between the points and the current I flowing between the points, measured in amperes, satisfy the relationship V=cI, where c is a constant. Which of the following best describes the relationship between the rate of change with respect to time t of the voltage and the rate of change with respect to time t of the current?
A \(\frac{\mathrm{d} V}{\mathrm{d} t}=I\frac{\mathrm{d} c}{\mathrm{d} t}\)
B \(\frac{\mathrm{d} V}{\mathrm{d} t}=c\frac{\mathrm{d} I}{\mathrm{d} t}\)
C \(\frac{\mathrm{d} V}{\mathrm{d} I}=c\)
D \(1=c\frac{\mathrm{d} I}{\mathrm{d} V}\)

Answer/Explanation

Ans:B

Question

A triangle has base b centimeters and height h centimeters, where the height is three times the base. Both b and h are functions of time t, measured in seconds. If A represents the area of the triangle, which of the following gives the rate of change of A with respect to t ?
A \(\frac{\mathrm{d} A}{\mathrm{d} t}\)=3bcm/sec
B \(\frac{\mathrm{d} A}{\mathrm{d} t}=2b \frac{\mathrm{d} b}{\mathrm{d} t}cm^{2}/sec\)
C \(\frac{\mathrm{d} A}{\mathrm{d} t}=3b \frac{\mathrm{d} b}{\mathrm{d} t}cm/sec\)
D \(\frac{\mathrm{d} A}{\mathrm{d} t}=3b \frac{\mathrm{d} b}{\mathrm{d} t}cm^{2}/sec\)

Answer/Explanation

Ans:D

Question

At a concert, a band is playing on a platform that extends P feet from a wall behind the band, and the platform is rising from ground level, as shown in the figure above. A light source is L feet from the wall, and the platform casts a lengthening shadow on the wall as the platform rises. At time t seconds, the platform is h feet above the ground, and the height of the shadow is s feet. The quantities are related by the equation \(\frac{1}{L}(h+s)=\frac{1}{P}s\) where L and P are constants. Which of the following best expresses the rate of change of h with respect to time in terms of the rate of change of s with respect to time?
A \(\frac{\mathrm{d} h}{\mathrm{d} t}=\frac{L}{P}s-s\)
B \(\frac{\mathrm{d} h}{\mathrm{d} t}=\frac{L}{P}s-\frac{\mathrm{d} s}{\mathrm{d} t}\)
C \(\frac{\mathrm{d} h}{\mathrm{d} t}=\frac{L}{P}\frac{\mathrm{d} s}{\mathrm{d} t}-s\)
D \(\frac{\mathrm{d} h}{\mathrm{d} t}=\frac{L}{P}\frac{\mathrm{d} s}{\mathrm{d} t}-\frac{\mathrm{d} s}{\mathrm{d} t}\)

Answer/Explanation

Ans:D

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