Gravitational potential energy and kinetic energy
5.2What the syllabus asks of you
- derive, using W = Fs, the formula ∆EP = mg∆h for gravitational potential energy changes in a uniform gravitational field
- recall and use the formula ∆EP = mg∆h for gravitational potential energy changes in a uniform gravitational field
- derive, using the equations of motion, the formula for kinetic energy EK = ½mv²
- recall and use EK = ½mv²
Read the notes first
Chapter 5: Gravitational potential energy and kinetic energy
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74 questions
1May / June 2026 · Paper 12 · Q18Show mark scheme →
A$4.1 \times 10^{6}\,\mathrm{m\,s^{-1}}$
B$5.8 \times 10^{6}\,\mathrm{m\,s^{-1}}$
C$8.1 \times 10^{6}\,\mathrm{m\,s^{-1}}$
D$1.2 \times 10^{7}\,\mathrm{m\,s^{-1}}$
Mark scheme
2May / June 2026 · Paper 13 · Q16Show mark scheme →
A1.8 m
B2.0 m
C2.2 m
D2.6 m
Mark scheme
3May / June 2026 · Paper 13 · Q18Show mark scheme →
AIt decreases in direct proportion to the displacement.
BIt does not change with the displacement.
CIt increases in direct proportion to the displacement.
DIt increases in direct proportion to the square of the displacement.
Mark scheme
4May / June 2026 · Paper 14 · Q16Show mark scheme →
Amgh
Bmgh + \frac{1}{2}mv^2
Cmgv
D\frac{mgv}{t}
Mark scheme
5May / June 2026 · Paper 14 · Q17Show mark scheme →
AGraph A: E_K against t, straight line through origin with positive gradient
BGraph B: E_K against t, curve through origin with decreasing gradient
CGraph C: E_K against t, curve through origin with increasing gradient
DGraph D: E_K against t, straight line with negative gradient starting from positive E_K
Mark scheme
6Oct / Nov 2025 · Paper 11 · Q17Show mark scheme →
A1 J
B10 J
C100 J
D10 000 J
Mark scheme
7Oct / Nov 2025 · Paper 12 · Q17Show mark scheme →
AF = ma
BW = Fs
CE = \frac{1}{2}Fs
Dv^2 = u^2 + 2as
Mark scheme
8Oct / Nov 2025 · Paper 12 · Q18Show mark scheme →
A0.6 m
B1.8 m
C2.4 m
D4.2 m
Mark scheme
9Oct / Nov 2025 · Paper 13 · Q17Show mark scheme →
A1 J
B10 J
C100 J
D10 000 J
Mark scheme
10Oct / Nov 2025 · Paper 14 · Q17Show mark scheme →
A0.87 m s–1
B2.3 m s–1
C2.5 m s–1
D3.4 m s–1
Mark scheme
11Oct / Nov 2025 · Paper 14 · Q19Show mark scheme →
AThe object must have a constant acceleration of 9.81 m s^{-2}.
BThe object must be travelling in a uniform gravitational field.
CThe object must be travelling only in a vertical direction.
DThe resultant force on the object must be equal to its weight.
Mark scheme
12May / June 2025 · Paper 11 · Q17Show mark scheme →
Amass and acceleration of free fall
Bmass and change in vertical displacement
Cweight and acceleration of free fall
Dweight and change in vertical displacement
Mark scheme
13May / June 2025 · Paper 11 · Q19Show mark scheme →
A\frac{(p_2^2 - p_1^2)}{2m}
B\frac{(p_2 - p_1)^2}{2m}
C\frac{p_2 - p_1}{2m}
D\frac{p_1 - p_2}{2m}
Mark scheme
14May / June 2025 · Paper 12 · Q18Show mark scheme →
A0.24 J
B1.8 J
C5.4 J
D11 J
Mark scheme
15May / June 2025 · Paper 13 · Q16Show mark scheme →
A3mgh
B6mgh
C8mgh
D10mgh
Mark scheme
16May / June 2025 · Paper 13 · Q18Show mark scheme →
AGraph A: $E_K$ against $h$, curve increasing from origin with increasing gradient
BGraph B: $E_K$ against $h$, straight line through origin with positive gradient
CGraph C: $E_K$ against $h$, curve decreasing from a maximum at $h=0$ to zero
DGraph D: $E_K$ against $h$, straight line decreasing from a maximum at $h=0$ to zero
Mark scheme
17May / June 2025 · Paper 13 · Q19Show mark scheme →
A4500 J
B6000 J
C24 000 J
D1 350 000 J
Mark scheme
18Feb / March 2025 · Paper 12 · Q15Show mark scheme →
A4.43√(Lcosθ)
B4.43√(Lsinθ)
C19.6Lcosθ
D19.6Lsinθ
Mark scheme
19Oct / Nov 2024 · Paper 11 · Q7Show mark scheme →
A4.65 kJ
B6.57 kJ
C135 kJ
D270 kJ
Mark scheme
20Oct / Nov 2024 · Paper 12 · Q18Show mark scheme →
A80 J
B170 J
C780 J
D1700 J
Mark scheme
21Oct / Nov 2024 · Paper 13 · Q17Show mark scheme →
A25 J
B35 J
C60 J
D95 J
Mark scheme
22Oct / Nov 2024 · Paper 13 · Q20Show mark scheme →
A1, 2 and 3
B1, 2 and 4
C1, 3 and 4
D2, 3 and 4
Mark scheme
23May / June 2024 · Paper 11 · Q20Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
24May / June 2024 · Paper 12 · Q16Show mark scheme →
A2
B4
C8
D16
Mark scheme
25May / June 2024 · Paper 12 · Q17Show mark scheme →
A0.13 J
B1.3 J
C130 J
D1300 J
Mark scheme
26May / June 2024 · Paper 13 · Q17Show mark scheme →
AGraph A: F against x, straight line through origin with positive gradient
BGraph B: F against x, straight line with positive gradient starting from positive F at x = 0
CGraph C: F against x, horizontal line at constant positive F
DGraph D: F against x, straight line with negative gradient starting from positive F at x = 0
Mark scheme
27Feb / March 2024 · Paper 12 · Q18Show mark scheme →
AEQ – ES
BES – ER
CET – EQ
DET – ER
Mark scheme
28Oct / Nov 2023 · Paper 11 · Q17Show mark scheme →
A30 J
B300 J
C3000 J
D30 000 J
Mark scheme
29Oct / Nov 2023 · Paper 12 · Q17Show mark scheme →
Aacceleration
Bmomentum
Cpower
Dwork done
Mark scheme
30Oct / Nov 2022 · Paper 11 · Q18Show mark scheme →
A4.1 × 10⁶ m s⁻¹
B5.8 × 10⁶ m s⁻¹
C8.1 × 10⁶ m s⁻¹
D1.2 × 10⁷ m s⁻¹
Mark scheme
31Oct / Nov 2022 · Paper 12 · Q19Show mark scheme →
A\frac{3}{4}g_X
B\frac{4}{3}g_X
C3g_X
D4g_X
Mark scheme
32Oct / Nov 2022 · Paper 13 · Q1Show mark scheme →
A10⁶ J
B10⁸ J
C10¹⁰ J
D10¹² J
Mark scheme
33Oct / Nov 2022 · Paper 13 · Q18Show mark scheme →
AIt decreases in direct proportion to the displacement.
BIt does not change with the displacement.
CIt increases in direct proportion to the displacement.
DIt increases in direct proportion to the square of the displacement.
Mark scheme
34May / June 2022 · Paper 11 · Q18Show mark scheme →
AGraph A: h decreasing curve from h-axis, concave up, approaching m-axis
BGraph B: straight line through origin with positive gradient
CGraph C: horizontal line (constant h)
DGraph D: increasing curve from origin, concave up
Mark scheme
35May / June 2022 · Paper 12 · Q18Show mark scheme →
A$F = ma$
B$W = Fs$
C$E = \frac{1}{2}Fs$
D$v^2 = u^2 + 2as$
Mark scheme
36May / June 2022 · Paper 13 · Q19Show mark scheme →
Amass for different objects moving at the same speed | kinetic energy
Bspeed for an object of constant mass | kinetic energy
Cvertical distance fallen for an object of constant mass | change of gravitational potential energy
Dmass for different objects falling the same vertical distance | change of gravitational potential energy
Mark scheme
37Feb / March 2022 · Paper 12 · Q17Show mark scheme →
A1.6 N
B390 N
C1.6 kN
D64 kN
Mark scheme
38Oct / Nov 2021 · Paper 11 · Q16Show mark scheme →
A0.33 J
B2.0 J
C2.1 J
D15 J
Mark scheme
39Oct / Nov 2021 · Paper 11 · Q17Show mark scheme →
A5.4 m s–1
B10 m s–1
C20 m s–1
D25 m s–1
Mark scheme
40Oct / Nov 2021 · Paper 12 · Q16Show mark scheme →
AAs it rises, its kinetic energy is transferred to gravitational potential energy.
BAt the midpoint of its path, its gravitational potential energy is equal to its initial kinetic energy.
CAt the top of its path, its kinetic energy is zero.
DAt the top of its path, its total energy is less than its initial total energy.
Mark scheme
41Oct / Nov 2021 · Paper 12 · Q19Show mark scheme →
ACar X has half the kinetic energy of car Y.
BCar X has one quarter of the kinetic energy of car Y.
CCar X has twice the kinetic energy of car Y.
DThe two cars have the same kinetic energy.
Mark scheme
42Oct / Nov 2021 · Paper 13 · Q18Show mark scheme →
A120 kJ
B240 kJ
C480 kJ
D960 kJ
Mark scheme
43May / June 2021 · Paper 12 · Q17Show mark scheme →
Amgs sinα / Fv
Bmv / Fs
Cmv² / 2Fs
Dmg sinα / F
Mark scheme
44May / June 2021 · Paper 13 · Q1Show mark scheme →
A40 J
B400 J
C4000 J
D40 000 J
Mark scheme
45Feb / March 2021 · Paper 12 · Q17Show mark scheme →
A0.023 J
B0.22 J
C23 J
D220 J
Mark scheme
46Oct / Nov 2020 · Paper 11 · Q8Show mark scheme →
Aforce of air resistance / acceleration
Bkinetic energy / time
Cpotential energy / height
Dwork done against air resistance / speed
Mark scheme
47Oct / Nov 2020 · Paper 11 · Q17Show mark scheme →
Athe decrease in gravitational potential energy of a mass of 60 kg when it moves vertically downwards through 40 m near the Earth’s surface
Bthe energy transferred in 15 s by a machine of power 160 W
Cthe kinetic energy of a mass of 12 kg moving at a speed of 20 m s–1
Dthe work done by a gas expanding against a constant external pressure of 120 kPa when its volume increases by 0.020 m3
Mark scheme
48Oct / Nov 2020 · Paper 12 · Q18Show mark scheme →
Akinetic energy = 1/2 × mass × (speed)²
Bmoment = force × distance
Cweight = mass × acceleration of free fall
Dwork done = power × time
Mark scheme
49Oct / Nov 2020 · Paper 13 · Q16Show mark scheme →
AMost of the kinetic energy is lost as heat and sound.
BThe kinetic energy decreases to zero and then returns to its original value.
CThe kinetic energy remains constant because it is an elastic collision.
DThe kinetic energy remains constant in magnitude but changes direction.
Mark scheme
50May / June 2020 · Paper 13 · Q1Show mark scheme →
A10 J
B100 J
C1000 J
D10 000 J
Mark scheme
51May / June 2020 · Paper 13 · Q18Show mark scheme →
A2.8 m s⁻¹
B3.2 m s⁻¹
C3.8 m s⁻¹
D14 m s⁻¹
Mark scheme
52Feb / March 2020 · Paper 12 · Q17Show mark scheme →
A60 J
B120 J
C140 J
D260 J
Mark scheme
53Oct / Nov 2019 · Paper 11 · Q17Show mark scheme →
A4500 J
B6000 J
C24 000 J
D1 350 000 J
Mark scheme
54Oct / Nov 2019 · Paper 13 · Q16Show mark scheme →
AGraph A: $E_p$ decreasing curve, $E_k$ constant horizontal line
BGraph B: $E_p$ decreasing straight line, $E_k$ constant horizontal line
CGraph C: $E_p$ decreasing curve, $E_k$ increasing curve
DGraph D: $E_p$ decreasing straight line, $E_k$ increasing straight line
Mark scheme
55Oct / Nov 2019 · Paper 13 · Q18Show mark scheme →
A$3\,mgh$
B$6\,mgh$
C$8\,mgh$
D$10\,mgh$
Mark scheme
56May / June 2019 · Paper 11 · Q18Show mark scheme →
AF = ma
Bs = vt
Cv^2 = u^2 + 2as
DW = Fs
Mark scheme
57May / June 2019 · Paper 12 · Q18Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
58May / June 2019 · Paper 13 · Q18Show mark scheme →
A15 J
B60 J
C120 J
D200 J
Mark scheme
59Oct / Nov 2018 · Paper 12 · Q17Show mark scheme →
AGraph A: $E_p$ increases linearly with $h$ from the origin
BGraph B: $E_p$ decreases linearly with $h$ from a maximum at $h=0$
CGraph C: $E_p$ rises to a maximum then decreases with $h$
DGraph D: $E_p$ decreases to a minimum then increases with $h$
Mark scheme
60May / June 2018 · Paper 11 · Q8Show mark scheme →
A\frac{(p_2^2 - p_1^2)}{2m}
B\frac{(p_2 - p_1)^2}{2m}
C\frac{p_2 - p_1}{2m}
D\frac{p_1 - p_2}{2m}
Mark scheme
61May / June 2018 · Paper 11 · Q15Show mark scheme →
A206 J
B641 J
C847 J
D1050 J
Mark scheme
62May / June 2018 · Paper 13 · Q16Show mark scheme →
AAs it rises, its kinetic energy is transferred to gravitational potential energy.
BAt the midpoint of its path, its gravitational potential energy is equal to its initial kinetic energy.
CAt the top of its path, its kinetic energy is zero.
DAt the top of its path, its total energy is less than its initial total energy.
Mark scheme
63Feb / March 2018 · Paper 12 · Q16Show mark scheme →
A0.30 m
B0.40 m
C0.50 m
D0.60 m
Mark scheme
64Feb / March 2018 · Paper 12 · Q18Show mark scheme →
ABoth boxes gain the same amount of gravitational potential energy and the same amount of work is done by the two forces.
BBoth boxes gain the same amount of gravitational potential energy but more work is done by the force acting on box Y than by the force acting on box X.
CBox Y gains less gravitational potential energy than box X because the weight of box Y is less than the weight of box X.
DBox Y gains more gravitational potential energy than box X as more work is done by the force acting on box Y than by the force acting on box X.
Mark scheme
65Oct / Nov 2017 · Paper 12 · Q18Show mark scheme →
ACar X has half the kinetic energy of car Y.
BCar X has one quarter of the kinetic energy of car Y.
CCar X has twice the kinetic energy of car Y.
DThe two cars have the same kinetic energy.
Mark scheme
66Oct / Nov 2017 · Paper 13 · Q18Show mark scheme →
Ah and M
BM, L and h
Cα, L, M
Dh only
Mark scheme
67May / June 2017 · Paper 11 · Q17Show mark scheme →
A1.0 × 10⁶ J
B2.0 × 10⁶ J
C1.0 × 10⁹ J
D2.0 × 10⁹ J
Mark scheme
68May / June 2017 · Paper 12 · Q17Show mark scheme →
A3.4 × 10^6 J
B6.8 × 10^6 J
C3.4 × 10^9 J
D6.8 × 10^9 J
Mark scheme
69May / June 2017 · Paper 13 · Q1Show mark scheme →
A1.5 × 10³ J
B1.5 × 10⁵ J
C1.5 × 10⁷ J
D1.5 × 10⁹ J
Mark scheme
70May / June 2017 · Paper 13 · Q16Show mark scheme →
A$\sqrt{v} \propto \dfrac{1}{m}$
B$v \propto \sqrt{m}$
C$v \propto \dfrac{1}{\sqrt{m}}$
D$\sqrt{v} \propto m$
Mark scheme
71Oct / Nov 2016 · Paper 12 · Q18Show mark scheme →
A15 J
B60 J
C120 J
D200 J
Mark scheme
72Oct / Nov 2016 · Paper 12 · Q19Show mark scheme →
A1.6
B2.6
C3.2
D4.0
Mark scheme
73May / June 2016 · Paper 11 · Q18Show mark scheme →
Athe decrease in gravitational potential energy of a body of mass 60 kg when it moves vertically downwards through 40 m near the Earth's surface
Bthe energy transferred in 15 s by a machine of power 160 W
Cthe kinetic energy of a body of mass 12 kg moving at a speed of 20 m s^-1
Dthe work done by a gas expanding against a constant external pressure of 120 kPa when its volume increases by 0.020 m^3
Mark scheme
74Feb / March 2016 · Paper 12 · Q16Show mark scheme →
A10 J
B100 J
C1000 J
D10 000 J
Mark scheme