Physics & Environmental Science — Final exam worked answers

Question 1 · 1 point

Trials are 1.8,2.0,2.2 s. Find mean.

Worked answer

2 s

6/3=2.

1 point for the correct objective answer; no written-method marks for this item.

Question 2 · 1 point

Which pair are both vector quantities?

1. Speed and distance
2. Velocity and force
3. Mass and time
4. Energy and temperature

Worked answer

Velocity and force

Vectors carry direction as well as magnitude.

1 point for the correct objective answer; no written-method marks for this item.

Question 3 · 3 points

Find resultant magnitude for 6 m east and 8 m north. Describe a measurement check.

Worked answer

10 m; a scale reference checks common bias.

√(6²+8²)=10. Compare repeated scale drawings with defined axes and resolution.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 4 · 3 points

Velocity rises from 2 to 14 m/s over 4 s. Find slope and interpret it.

Worked answer

3 m/s² for a linear velocity-time segment.

(14−2)/4; velocity divided by time gives acceleration units.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 5 · 1 point

A jogger runs 8 km east, then turns around and runs 5 km west along the same road. What total distance did she cover?

Worked answer

13 km

Distance is total path length: 8 + 5 = 13 km.

1 point for the correct objective answer; no written-method marks for this item.

Question 6 · 1 point

A car rounds a bend at constant speed. It is

1. not accelerating
2. accelerating, because its direction changes
3. decelerating
4. in equilibrium

Worked answer

accelerating, because its direction changes

Velocity includes direction, so changing direction is acceleration.

1 point for the correct objective answer; no written-method marks for this item.

Question 7 · 3 points

An object starts at rest and accelerates at 2 m/s² for 5 s. Find velocity and displacement.

Worked answer

10 m/s and 25 m.

v=at; x=½at².

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 8 · 3 points

A horizontal projectile has vx=6 m/s and falls for 2 s. Find range and drop with g=9.8.

Worked answer

12 m range and 19.6 m drop.

Range=vxt; drop=½gt², neglecting air resistance.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 9 · 1 point

A net force of 36 N acts on a 4 kg block on a frictionless surface. Find its acceleration.

Worked answer

9 m/s²

a = ΣF ÷ m = 36 ÷ 4 = 9 m/s².

1 point for the correct objective answer; no written-method marks for this item.

Question 10 · 1 point

An object moves at constant velocity. The net force on it is

1. zero
2. constant and non-zero
3. increasing
4. equal to its weight

Worked answer

zero

No change in velocity means no net force, though individual forces may be large.

1 point for the correct objective answer; no written-method marks for this item.

Question 11 · 3 points

A 5 kg object has 30 N right and 10 N left. Find acceleration.

Worked answer

4 m/s² right.

Net=20 N right; divide by mass.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 12 · 3 points

A 4 N perpendicular force acts 0.30 m from a pivot. Find torque and state static-equilibrium conditions.

Worked answer

1.2 N·m; balance forces and torques.

τ=rF=1.2; both ΣF=0 and Στ=0 are needed.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 13 · 1 point

A 30 N force pushes a box 3.0 m in the direction of the force. How much work is done?

Worked answer

90 J

W = Fd = 30 × 3.0 = 90 J.

1 point for the correct objective answer; no written-method marks for this item.

Question 14 · 1 point

Doubling an object's speed changes its kinetic energy by a factor of

1. 2
2. 3
3. 4
4. 8

Worked answer

4

Kinetic energy depends on the square of the speed.

1 point for the correct objective answer; no written-method marks for this item.

Question 15 · 3 points

A 2 kg object is 4 m above a chosen zero; g=9.8. Find potential energy and ideal speed after falling from rest.

Worked answer

78.4 J and about 8.85 m/s.

U=mgh=78.4 J; v=√(2gh).

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 16 · 3 points

A 0.5 kg ball changes velocity +4 to −2 m/s in 0.10 s. Find impulse and average force.

Worked answer

−3 N·s and −30 N.

Δp=0.5(−2−4); Favg=Δp/Δt.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 17 · 1 point

A wave has a frequency of 10 Hz and a wavelength of 3 m. Find its speed.

Worked answer

30 m/s

v = f × λ = 10 × 3 = 30 m/s.

1 point for the correct objective answer; no written-method marks for this item.

Question 18 · 1 point

For a wave of fixed speed, increasing the frequency

1. increases the wavelength
2. decreases the wavelength
3. leaves the wavelength unchanged
4. increases the amplitude

Worked answer

decreases the wavelength

Speed equals frequency times wavelength, so the two trade off.

1 point for the correct objective answer; no written-method marks for this item.

Question 19 · 3 points

A string fixed at both ends has L=1 m and v=40 m/s. Find first two harmonics.

Worked answer

20 Hz and 40 Hz.

f₁=v/(2L); f₂=2f₁.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 20 · 3 points

Light goes from index 1.5 toward index 1.0. State total-internal-reflection conditions and find critical angle.

Worked answer

θc≈41.8°; total internal reflection for greater incidence angles in the ideal model.

Initial index must be larger; sinθc=1/1.5; measure angles from the normal.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 21 · 1 point

Two small spheres both carry a positive charge. The electric force between them is:

1. attractive
2. repulsive
3. zero
4. always gravitational

Worked answer

repulsive

Like charges repel, so two positive charges push apart.

1 point for the correct objective answer; no written-method marks for this item.

Question 22 · 1 point

Two identical resistors in series compared with one alone give a total resistance that is

1. halved
2. unchanged
3. doubled
4. zero

Worked answer

doubled

Series resistances add.

1 point for the correct objective answer; no written-method marks for this item.

Question 23 · 3 points

Two 12 Ω resistors are parallel on 6 V. Find total current and power.

Worked answer

1 A and 6 W.

Equivalent resistance=6 Ω; I=V/R; P=VI.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 24 · 3 points

Find energy stored in a 100 μF capacitor at 10 V.

Worked answer

0.005 J; this is a paper calculation, not a device-handling activity.

Convert to 0.000100 F; U=½CV².

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 25 · 1 point

Photon 5 eV, work function 2 eV. Find Kmax.

Worked answer

3 eV

5−2=3.

1 point for the correct objective answer; no written-method marks for this item.

Question 26 · 1 point

Higher-frequency electromagnetic radiation carries

1. less energy per photon
2. more energy per photon
3. the same energy per photon
4. no energy

Worked answer

more energy per photon

Photon energy rises with frequency, which is why ultraviolet damages tissue and radio does not.

1 point for the correct objective answer; no written-method marks for this item.

Question 27 · 3 points

A 4 eV photon hits a surface with work function 2.5 eV. Find maximum electron energy and stopping potential.

Worked answer

1.5 eV and 1.5 V.

Kmax=4−2.5; electron energy in eV corresponds numerically to stopping volts.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 28 · 3 points

A proper interval is 8 s at γ=1.25. Find other-frame interval. Separately, find nuclear energy for 0.010 u mass loss at 931.5 MeV/u.

Worked answer

10 s; 9.315 MeV.

Δt=γΔτ; Q=0.010×931.5 in the separate nuclear model.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 29 · 1 point

In an energy pyramid, which trophic level has the LEAST energy available to it?

1. Primary consumers
2. Secondary consumers
3. Top predators
4. Producers

Worked answer

Top predators

Because only ~10% of energy transfers at each step, the top predators at the peak have the least energy available.

1 point for the correct objective answer; no written-method marks for this item.

Question 30 · 1 point

A population levels off at its carrying capacity because

1. reproduction stops
2. density-dependent factors increasingly limit growth
3. predators vanish
4. the habitat grows

Worked answer

density-dependent factors increasingly limit growth

Competition, disease and resource limits intensify as density rises.

1 point for the correct objective answer; no written-method marks for this item.

Question 31 · 3 points

Two ecological species have fractions 0.25 and 0.75. Find D=1−Σpi².

Worked answer

0.375; index definition and equal sampling effort matter.

1−(0.0625+0.5625).

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 32 · 3 points

N=1000, r=0.2/year, K=2000. Find instantaneous logistic rate. Is it the exact next-year increase?

Worked answer

100 individuals/year at that moment; not an exact integrated annual increase.

rN(1−N/K)=0.2×1000×0.5; the rate changes with population.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 33 · 1 point

Which of the following is a fossil fuel?

1. Wind
2. Coal
3. Uranium
4. Sunlight

Worked answer

Coal

Coal, oil, and natural gas are the three fossil fuels. Uranium is a nuclear fuel, and sunlight and wind are renewable.

1 point for the correct objective answer; no written-method marks for this item.

Question 34 · 1 point

The main limitation of 'reserves divided by current use' as a lifetime estimate is that it assumes

1. prices are fixed
2. use stays constant and no new reserves are found
3. the resource is renewable
4. extraction is free

Worked answer

use stays constant and no new reserves are found

Both assumptions are usually false, so the figure is indicative only.

1 point for the correct objective answer; no written-method marks for this item.

Question 35 · 3 points

A 2 kW generator delivers 18 kWh in 24 h. Find capacity factor and distinguish efficiency.

Worked answer

37.5%; conversion efficiency is a different ratio.

18/(2×24)=0.375; capacity factor compares rated-time output, not input energy.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 36 · 3 points

A reservoir starts at 1000 units with annual input 120 and output 150. Find storage change and final amount.

Worked answer

−30 units; 970 remain within the defined annual boundary.

Change=input−output=−30; add to starting storage.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 37 · 1 point

Which of the following is an example of nonpoint-source pollution?

1. A pipe discharging waste from a single factory into a river
2. Smoke pouring from one power plant's smokestack
3. Fertilizer and motor oil washing off lawns and roads across a whole watershed
4. Untreated sewage released from one broken outfall pipe

Worked answer

Fertilizer and motor oil washing off lawns and roads across a whole watershed

Nonpoint-source pollution comes from many scattered, hard-to-identify sources at once, like runoff spread across an entire watershed, rather than from a single identifiable outlet.

1 point for the correct objective answer; no written-method marks for this item.

Question 38 · 1 point

A single unusually hot year is weak evidence of a climate trend because

1. thermometers are unreliable
2. year-to-year variation is large and a trend is a change in the long-run average
3. heat is not measurable
4. one year is too cold

Worked answer

year-to-year variation is large and a trend is a change in the long-run average

Trends are established over decades and across the globe.

1 point for the correct objective answer; no written-method marks for this item.

Question 39 · 3 points

Modeled pH falls from 8.2 to 8.1. Find the hydrogen-ion factor and explain acidification while remaining basic.

Worked answer

About 1.26 times; both values remain above pH 7.

Factor=10^0.1≈1.26; acidification means declining pH.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 40 · 3 points

Anomaly rises from 0.3 to 0.9°C in 30 years. Find trend per decade and one attribution limitation.

Worked answer

0.20°C/decade; mechanisms and independent driver comparisons are needed.

0.6/30×10; trend alone does not isolate competing causes.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 41 · 1 point

Which listed activity directly removes habitat and separates remaining habitat patches?

1. Scientists collecting a few specimens for study
2. Natural predators hunting their usual prey
3. Zoos keeping some animals in captivity
4. Habitat loss and fragmentation from clearing and dividing land

Worked answer

Habitat loss and fragmentation from clearing and dividing land

Clearing and dividing land can reduce available habitat and connectivity. The relative importance of threats varies among ecosystems and requires evidence.

1 point for the correct objective answer; no written-method marks for this item.

Question 42 · 1 point

Comparing two environmental options by cost per tonne of carbon saved is incomplete because it ignores

1. the arithmetic
2. who bears the cost, reliability and side effects
3. the units
4. the total emissions

Worked answer

who bears the cost, reliability and side effects

Cost-effectiveness is one criterion among several in a real decision.

1 point for the correct objective answer; no written-method marks for this item.

Question 43 · 3 points

Habitat area falls from 8000 to 2000 ha. Find percent loss and propose a monitored conservation measure.

Worked answer

75%; for example protect connected habitat and monitor occupancy, recruitment, and threats.

Loss=6000/8000×100%; connect an intervention to species needs and a measurable outcome.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 44 · 3 points

An upgrade costs 400 currency units and saves 50 kWh/year at 0.20/kWh. Find simple payback and a design limitation.

Worked answer

40 years in this simplified model; lifespan, maintenance, and service assumptions can change feasibility.

Savings=10 units/year; payback=400/10.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.