DC-IC Flashcards
1
Q
- The air in a certain cylinder is at a pressure of 25.5 kPa when its volume is
146 cm3
. Find the rate of change of the pressure with respect to the volume
as the piston descends farther.
Hint use Boyle’s Law.
A. -0.175 kPa/cm C. -0.180 kPa/cm
B. -0.185 kPa/cm D. -0.190 kPa/cm
A
A. -0.175 kPa/cm
2
Q
- A certain light source produces an illumination of 655 lux on a surface at a distance of 2.75 m. Find the rate of change of illumination with respect to distance, and evaluate it at 2.75 m.
A. -529.6 lux/m C. -476.4 lux/m
B. -352.9 lux/m D. -414.8 lux/m
A
C. -476.4 lux/m
3
Q
- The period (in seconds) for a pendulum of length L cm to complete one oscillation is equal t to P=0.224√L. Find the rate of change of the period with respect to length when the length is 23.0 cm.
A. 0.0113 s/cm C. 0.0234 s/cm
B. 0.0365 s/cm D. 0.0429 s/cm
A
C. 0.0234 s/cm
4
Q
- The power dissipated in a certain resistor is 865 W at a current of 2.48 A. What is the rate of change of the power with respect to the current as current starts to increase? Hint: P = I^2 R
A. 3.62 W/A C. 4.96 W/A
B. 5.23 W/A D. 5.85 W/A
A
C. 4.96 W/A
5
Q
- The temperature T at a distance x cm from the end of a certain heated bar
is given by T= 2.24x^3+ 1.85x + 95.4 (°C). Find the rate of change of
temperature with respect to distance at a point 3.75 cm from the end.
A. 65.77 °C/cm C. 72.49 °C/m
B. 86.31 °C/m D. 96.35 °C/m
A
D. 96.35 °C/m
6
Q
The cantilever beam in the figure has a deflection y at a distance x from the
built-in end of
𝑦 =𝑤𝑥²/24𝐸𝐼 (𝑥² + 6𝐿² − 4𝐿𝑥)
A
A. 𝑤𝑥/6𝐸𝐼 (𝑥²+ 3𝐿 − 3𝐿𝑥)
7
Q
- A 20.0 ft ladder leans against a building. The foot of the ladder is pulled away from the building at a rate of 2.00 ft/s. How fast is the top of the ladder falling when its foot is 10.0 ft from the building?
A. 1.15 ft/s C. 3.46 ft/s
B. -1.15 ft/s D. -3.46 ft/
A
B. -1.15 ft/s
8
Q
- A conical tank with vertex down has a base radius of 3.00 m and a height
of 6.00 m. Water flows at a rate of 2.00 m3/h. How fast is the water level rising
when the depth y is 3.00 m?
A. 0.382 m/h C. 0.238 m/h
B. 0.328 m/h D. 0.283 m/h
A
D. 0.283 m/h
9
Q
- Ship A leaves a port P and travels west at 11.5 km/h. After 2.25 h, ship B leaves P and travels north at 19.4 km.h. How fast are the ships separating 5.00 h after the departure of A?
A. 21.6 km/h C. 22.6 km/h
B. 26.1 km/h D. 26.2 km/h
A
A. 21.6 km/h
10
Q
- An airplane flying horizontally at a height of 8000 m and at a rate of 100
m/s passes directly over a pond. How fast is its straight-line distance from the
pond increasing 1 min later?
A. 75 m/s C. 60 m/s
B. 80 m/s D. 55 m/s
A
C. 60 m/s
11
Q
- A person is running at a rate of 12.0 km/h on a horizontal street directly
toward the foot of a tower 30.0 m high. How fast is the person approaching the
top of the tower when 15.0 m from the foot?
A. 7.35 m/s C. 7.53 m/s
B. 3.57 m/s D. 5.37 m/s
A
D. 5.37 m/s
12
Q
- A boat with its anchor on the bottom at a depth of 40.0 m is drifting away
from the anchor at 4.00 m/s, while the anchor cable slips from the boat at water
level. At what rate is the cable leaving the boat when 50.0 m of cable is out?
Assume that the cable is straight.
A. 2.40 m/s C. 4.20 m/s
B. 3.20 m/s D. 2.30 m/s
A
A. 2.40 m/s
13
Q
- A lamp is located on the ground 10.0m from a building. A person 2.00 m
tall walks from the light toward the building at a rate of 2.00 m/s. Find the rate
at which the person’s shadow on the wall is shortening when the person is
5.00 m from the building.
A. 1.60 m/s C. 2.50 m/s
B. -1.60 m/s D. -2.50 m/s
A
B. -1.60 m/s
14
Q
- A square sheet of metal 10.0 cm on a side is expanded by increasing its
temperature so that each side of the square increases at 0.005 00 cm/s. At
what rate is the area of the square increasing at 20.0 s?
A. 0.204 cm2/s C. 0.101 cm2/s
B. 0.202 cm2/s D. 0.102 m/s
A
C. 0.101 cm2/s
15
Q
- The volume of a cube is increasing at 10.0 cm3
/min. At the instant when
its volume is 125 cm2
, what is the rate of change of its edge length?
A. 7.5 cm/min C. 0.133 cm/min
B. 2.5 cm/min D. 0.267 cm/min
A
C. 0.133 cm/min
16
Q
- At some instant the diameter x of a cylinder is 10.0 cm and is increasing
at a rate of 1.00 cm/min. At the same instant, the height y is 20.0 cm and is
decreasing at a rate (dy/dt) such that the volume is not changing, dV/dt = 0.
Find dy/dt.
A. 4.00 cm/min C. 8.00 cm/min
B. -4.00 cm/min D. -8/00 cm/min
A
B. -4.00 cm/min
17
Q
- A horizontal trough 5.00m long has ends in the shape of an isosceles right
triangle. If water is poured into it at the rate of 0.500 m3/min, at what rate is
the surface of the water rising when the water is 1.00 m deep?
A. 0.0005 m/min C. 0.0050 m/min
B. 0.5000 m/min D. 0.0500 m/min
A
D. 0.5000 m/min
18
Q
- As a man walks a distance x along a board, he sinks a distance y in., where
𝑦 =𝑃𝑥³/3𝐸𝐼
A. 1.61 in./s C. 1.16 in./s
B. 0.54 in./s D. 0.45 in./s
A
A. 1.61 in./s
19
Q
- An open-top box is to be made from a square of sheet metal 40cm on a
side by cutting a square from each corner and bending up the sides along the
dashed lines. Find the dimension x of the cutout that will result in a box of the
greatest volume.
A. 20 cm C. 6.67 cm
B. 40 cm D. 14.33 cm
A
C. 6.67 cm
20
Q
- A rectangular garden laid out along your neighbour’s lot contains 432 m2.
It is to be fenced on all sides. If the neighbour pays for half the shared fence,
what should be the dimensions of the garden so that your cost is minimum?
A. 18 m x 24 m C. 36 m x 12 m
B. 16 m x 27 m D. 32 m x 13.5 m
A
A. 18 m x 24 m
21
Q
- A rectangular pasture 162 m2 in area is built so that a long, straight wall
serves one side of it. If the length of the fence along the remaining three sides
is the least possible, find the dimensions of the pasture.
A. 6 m x 27 m C. 4.5 m x 36 m
B. 12 m x 13.5 m D. 9 m x 18 m
A
D. 9 m x 18 m
22
Q
- Find the volume of the largest open-top box that can be made from a
rectangular sheet of metal 6.00 cm by 16.00 cm by cutting a square from each
corner and turning up the sides.
A. 29.63 cm3 C. 18.96 cm3
B. 59.26 cm3 D. 66.37 cm3
A
B. 59.26 cm3
23
Q
- A gutter is to be made of a strip of metal 30.0 cm wide, with the cross
section having the form shown. What depth x gives a maximum cross-
sectional area?
A. 5 cm C. 8.66 cm
B. 7.07 cm D. 2.59 cm
A
C. 8.66 cm
24
Q
- A man in a rowboat at P, 6.00 km from the shore, desires to reach point Q
on the shore at a straight-line distance of 10.0 km from his present position. If
he can walk 4km/h and row 3.00 km/h, at what point L should he land in order
to reach Q in the shortest time?
A. 3.3 km C. 4.7 km
B. 6.8 km D. 1.2 km
A
B. 6.8 km
25
25. The intensity E of illumination at a point, from a light source at a distance
x from the point, is given by 𝐸=𝑘𝐼/𝑥². At what distance
from M is the total illumination a minimum?
A. 59.1 km C. 95.1 km
B. 91.5 km D. 51.9 km
A. 59.1 km
26
1. Find the average ordinate of a half-cycle of the sinusoidal voltage
𝑣 = 𝑉 𝑠𝑖𝑛𝜃
A. 0.736 V C. 0.637 V
B. 0.763 V D. 0.376 V
C. 0.637 V
27
2. Find the root mean square value of the sinusoidal voltage
𝑣 = 𝑉 𝑠𝑖𝑛𝜃
A. 0.770 V C. 0.707 V
B. 0.070 V D. 0.700 V
C. 0.707 V
28
SITUATION. A flywheel in a machine starts from rest and accelerates at 3.85t
rad/s2.
3. Find the angular velocity after 10.0s.
A. 193 rad/s C. 139 rad/s
B. 385 rad/s D. 358 rad/s
A. 193 rad/s
29
4. Find the total number of revolutions after 10.0 s.
A. 642 C. 102
B. 1925 D. 306
C. 102
31
6. Find the area bounded by the curves 𝑦² = 12𝑥 and 𝑦² = 24𝑥 − 36.
A. 6 C. 3
B. 12 D. 9
B. 12
32
7. The first-quadrant area bounded by the curve y=x^2, the y axis, and the line
y = 4 is rotated about the line x=3.
A. 21π C. 23π
B. 22 π D. 24π
D. 24π
33
8. A certain spring has a free length (when no force is applied) of 10.0 cm. The
spring constant is 12.0 N/cm. Find the work needed to stretch the spring from
a length of 12.0cm to a length of 14.0 cm.
A. 312 C. 48
B. 72 D. 96
B. 72
34
5. Find the area bounded by the curve 𝑦 = 𝑥
2 − 4 and the x axis between x
= 1 and 3.
A. 2/3 C. 10/3
B. 4 D. 5
B. 4
