Kinetic and Potential Energy Worksheet with Answers - Laney Lee - Free Printable

Let’s go step by step through each part of the worksheet.

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Part 1: Analyzing the graph (ball rolling from A to G)

We need to remember:
- Kinetic energy (KE) is highest when the ball is moving fastest → that happens at the *lowest* points on the track (because potential energy turns into kinetic energy as it rolls down).
- Potential energy (PE) is highest when the ball is at the *highest* point (because height = more stored energy).
- When PE increases, KE decreases (and vice versa), because total energy stays mostly the same (ignoring friction).

Looking at the graph:

Points in order: A → B → C → D → E → F → G
Heights (approximate from graph):
- A: medium high
- B: low
- C: medium
- D: lowest → max KE, min PE
- E: medium low
- F: high
- G: medium

Actually, let’s look again carefully — the graph shows a wavy path. Let’s list heights from highest to lowest based on vertical position:

Highest: F
Then: A, C, G
Then: E
Then: B
Lowest: D ← this is the bottom of the valley

So:

1. Maximum kinetic energy? → At the lowest point → D

2. Maximum potential energy? → At the highest point → F

3. Least kinetic energy? → When it’s slowest → at the highest point → F (since all energy is potential there)

4. Least potential energy? → At the lowest point → D

5. Sequence showing increase in potential energy?
That means going UP the hill → gaining height → so PE goes up.
Look for sequences where the ball moves to higher points.

Check options:
a. D,E,F → D(low) → E(med-low) → F(high) → YES, increasing height → increasing PE
b. B,F,E,C → B(low) → F(high) → E(med-low) → C(med) → not consistently increasing
c. D,E,F,G → D→E→F→G: D(low), E(up a bit), F(very high), G(down a bit) → not strictly increasing
d. A,G,F,C → A→G→F→C: A(med), G(med), F(high), C(med) → no

Only a. D,E,F shows clear increase in height → increase in PE.

Wait — option c is D,E,F,G — but G is lower than F, so PE decreases at the end. So only a is fully increasing.

But let’s check the answer choices again — maybe I misread.

Option a: D,E,F → yes, increasing
Option c: D,E,F,G → ends with drop → not pure increase
So correct is a

BUT wait — looking back at the graph, after F it goes to G which is lower, so D→E→F is increasing, then F→G is decreasing.

So question 5: “increase in potential energy” — meaning overall trend or each step? Probably each step must be increasing.

So D→E→F: each step up → good.

Now question 6: increase in kinetic energy → that means speeding up → going DOWN the hill.

Which sequence shows that?

a. D,E,F → D(lowest) → E(up) → F(higher) → slowing down → KE decreasing → NO
b. A,B,E,D → A→B (down) → B→E (up?) Wait, let’s map positions.

Actually, let’s trace the path:

From A to B: down → KE increases
B to C: up → KE decreases
C to D: down → KE increases
D to E: up → KE decreases
E to F: up → KE decreases
F to G: down → KE increases

So for increase in KE: we want downward slopes.

Option b: A,B,E,D → A→B (down, KE↑), B→E? From B to E — B is low, E is higher than B? Looking at graph: B is near bottom, E is above B but below C? Actually, from B to C to D to E — so B to E is not direct. The sequence given is A,B,E,D — that skips C and D? That doesn’t make sense physically unless it’s just listing points in order visited.

The problem says "sequence" — probably meaning consecutive points along the path.

So valid sequences should be consecutive letters.

Option b: A,B,E,D — not consecutive! A to B is ok, but B to E skips C and D — invalid? Or maybe it's just the order of points, not necessarily adjacent.

This is ambiguous. But likely, they mean the order the ball visits them.

Ball goes A→B→C→D→E→F→G

So possible sequences are sub-sequences of that.

Option b: A,B,E,D — but E comes after D, so A,B,E,D would be out of order. Probably not intended.

Let me re-read the options:

5. Which sequence correctly shows an increase in potential energy?
a. D,E,F
b. B,F,E,C
c. D,E,F,G
d. A,G,F,C

For 5, a. D,E,F — D to E to F: if E is higher than D, and F higher than E, then yes.

Similarly for 6: increase in kinetic energy — need downward motion.

Option d for 6: A,B,C,D — A to B (down), B to C (up? wait no — from graph, after B it goes up to C? Let me visualize.

Typical roller coaster graph: starts at A (high), goes down to B (low), up to C (medium), down to D (lowest), up to E (medium), up to F (high), down to G (medium).

So:

A to B: down → KE ↑
B to C: up → KE ↓
C to D: down → KE ↑
D to E: up → KE ↓
E to F: up → KE ↓
F to G: down → KE ↑

So for increase in KE: segments like A-B, C-D, F-G

Now look at option d for question 6: A,B,C,D — that includes A-B (KE↑), B-C (KE↓), C-D (KE↑) — not purely increasing.

Option a: D,E,F — all uphill → KE decreasing

Option b: A,B,E,D — messy

Option c: C,E,F,G — C to E? Not direct; C to D to E — C to D is down (KE↑), D to E is up (KE↓), etc.

Perhaps the best is to think of net change or consistent direction.

Maybe for question 6, "increase in kinetic energy" means the ball is gaining speed overall in that sequence.

But let's look at standard answers for such graphs.

I recall that in many textbooks, for a similar graph:

- Max KE at lowest point: D
- Max PE at highest point: F
- Min KE at highest point: F
- Min PE at lowest point: D

For sequences:

Increase in PE: moving upward — e.g., D to E to F (if E is between D and F in height)

In the graph, from D to E to F: D is lowest, E is higher than D, F is higher than E — so yes, PE increases.

Similarly, increase in KE: moving downward — e.g., F to G, or A to B, or C to D.

Look at option d for question 6: A,B,C,D — but B to C is upward, so KE decreases there.

Option b: A,B,E,D — not sequential.

Perhaps option d is meant to be A to B to C to D, but that has ups and downs.

Another idea: perhaps "sequence" means the order, and we see if PE or KE is increasing over that path.

For question 6, option d: A,B,C,D — let's calculate net change.

At A: some PE, some KE
At B: less PE, more KE
At C: more PE than B, less KE than B
At D: least PE, most KE

So from A to D, KE increases overall, but not monotonically.

But the question says "shows an increase", which might allow non-monotonic, but typically in such questions, they want consistently increasing.

Let's check online or standard interpretation.

Since this is a common type, I'll assume:

For increase in KE: the sequence where the ball is generally going down.

Option d: A,B,C,D — starts high, ends low, so net increase in KE.

Similarly, for PE, D,E,F starts low, ends high.

But let's see the answer choices provided.

Perhaps for question 6, the correct answer is d. A,B,C,D because from A to D, the ball loses height overall, so gains KE.

Similarly, for question 7: decrease in potential energy — that would be when height decreases.

Option c for 7: D,E,F,G — D to E to F to G: D(low), E(higher), F(highest), G(lower) — so PE increases then decreases, not pure decrease.

Option d for 7: G,F,C,D — G to F (up? F is higher than G? In graph, F is peak, G is after, so F to G is down, but G to F would be up — but the sequence is G,F,C,D — so G to F: if F is higher, PE increases, then F to C: down, PE decreases, etc.

This is confusing.

Let me try to assign approximate heights:

Assume y-axis values:

A: 4
B: 1
C: 3
D: 0 (lowest)
E: 2
F: 5 (highest)
G: 3

So:

1. Max KE: at min height → D (y=0) → D

2. Max PE: at max height → F (y=5) → F

3. Least KE: at max height → F → F (since velocity is zero at top if it stops, but in rolling, it may not be zero, but usually in these problems, at highest point KE is min)

4. Least PE: at min height → D → D

5. Increase in PE: sequence where height increases.

a. D,E,F: y=0→2→5 → increasing → yes
b. B,F,E,C: 1→5→2→3 → not increasing
c. D,E,F,G: 0→2→5→3 → increases then decreases
d. A,G,F,C: 4→3→5→3 → not increasing

So only a is strictly increasing → a

6. Increase in KE: since KE proportional to v^2, and v increases when height decreases (conservation of energy), so when height decreases, KE increases.

So sequence where height decreases.

a. D,E,F: 0→2→5 → height increasing → KE decreasing
b. A,B,E,D: 4→1→2→0 → not monotonic; 4 to 1 (decrease), 1 to 2 (increase), 2 to 0 (decrease) — not pure increase in KE
c. C,E,F,G: 3→2→5→3 → 3 to 2 (decrease, KE↑), 2 to 5 (increase, KE↓), 5 to 3 (decrease, KE↑) — mixed
d. A,B,C,D: 4→1→3→0 → 4 to 1 (↓, KE↑), 1 to 3 (↑, KE↓), 3 to 0 (↓, KE↑) — mixed

None are purely decreasing in height. But perhaps they mean the net effect or the dominant trend.

Option d: A to D, height from 4 to 0, so net decrease, so net increase in KE.

Similarly, in many sources, for such a sequence, they accept it if the final point is lower than initial.

But let's see the options — perhaps b is A,B,E,D — but E is after D in time, so not logical.

Another thought: perhaps the sequence is the order visited, and for increase in KE, they want a segment where it's going down continuously.

For example, C to D is down, but not in options.

Look at option d for 6: A,B,C,D — but B to C is up.

Unless the graph is different. Perhaps from A to B down, B to C is still down? No, typically it's up to C.

I think there might be a mistake in my assumption.

Let me search for a standard answer or rethink.

Perhaps for question 6, "increase in kinetic energy" means the ball is accelerating, which is when going down, so any downward slope.

But the sequence must show that.

Option b: A,B,E,D — if we interpret as the ball going from A to B (down, KE↑), then to E — but E is after D, so not possible.

Perhaps the letters are not in order, but the sequence is listed as the path.

I think the intended answer for 6 is d. A,B,C,D, assuming that from A to D, it's mostly down, but it's not.

Let's calculate the change.

From A to B: Δh = -3, so ΔKE = +3g (approximately)
B to C: Δh = +2, ΔKE = -2g
C to D: Δh = -3, ΔKE = +3g
Net from A to D: Δh = -4, so net ΔKE = +4g, so overall increase.

Similarly, for other sequences.

For question 7: decrease in potential energy — net decrease in height.

Option c: D,E,F,G: 0→2→5→3, net +3, so PE increase
Option d: G,F,C,D: 3→5→3→0, net -3, so PE decrease

Yes! G to F: 3 to 5, PE increase; F to C: 5 to 3, PE decrease; C to D: 3 to 0, PE decrease; net from G to D: 3 to 0, decrease of 3, so net decrease in PE.

And for question 8: decrease in kinetic energy — net increase in height, so loss of KE.

Option a: G,F,D: G(3) to F(5) to D(0) — 3 to 5 (PE↑, KE↓), 5 to 0 (PE↓, KE↑) — net from G to D: 3 to 0, so net KE increase, not decrease.

Option b: B,F,E,C: B(1) to F(5) to E(2) to C(3) — 1 to 5 (KE↓), 5 to 2 (KE↑), 2 to 3 (KE↓) — net from B to C: 1 to 3, so net PE increase, net KE decrease.

Height from 1 to 3, so Δh = +2, so ΔKE = -2g, so decrease in KE.

Similarly, option c: D,E,F,G: 0 to 2 to 5 to 3, net +3, so KE decrease.

Option d: G,F,C,D: 3 to 5 to 3 to 0, net -3, so KE increase.

So for question 8, both b and c show net decrease in KE, but let's see which one is listed.

Option b: B,F,E,C — net height change: B1 to C3, +2, so KE decrease.

Option c: D,E,F,G — D0 to G3, +3, KE decrease.

But the question is "correctly shows a decrease", and both do, but perhaps they want the sequence where it's consistently decreasing or something.

In option b: B to F: KE decreases (height increases), F to E: height decreases, KE increases, E to C: height increases from 2 to 3, KE decreases — so not consistent.

In option c: D to E: height 0 to 2, KE decreases; E to F: 2 to 5, KE decreases; F to G: 5 to 3, KE increases — so first two steps KE decrease, last step increases.

Net decrease, but not throughout.

Perhaps the best is to choose the one with the largest net decrease or something.

But let's look back at the answer choices for 8:

a. G,F,D
b. B,F,E,C
c. D,E,F,G
d. G,F,C,D

For c: D,E,F,G — as above, net height increase, so net KE decrease.

For b: B,F,E,C — net height increase from 1 to 3, so net KE decrease.

But in b, from F to E, height decreases, so KE increases, which is opposite.

Whereas in c, from D to E to F, height increases steadily, so KE decreases steadily, then F to G, height decreases, KE increases, so only the first part is decrease.

Perhaps the intended answer is c for 8, as D to F is increase in PE, decrease in KE.

I recall that in some worksheets, for such a graph, the answers are:

1. D
2. F
3. F
4. D
5. a (D,E,F)
6. d (A,B,C,D) — even though not monotonic, net increase
7. d (G,F,C,D) — net decrease in PE
8. c (D,E,F,G) — net decrease in KE? No, net increase in PE, so net decrease in KE.

For 8, decrease in KE means net loss of KE, which happens when net gain in PE, i.e., net increase in height.

So for c: D to G, height 0 to 3, increase, so KE decrease.

For b: B to C, 1 to 3, increase, KE decrease.

But let's see the options; perhaps c is chosen because it's a longer sequence or something.

Maybe for 8, "decrease in kinetic energy" and the sequence D,E,F,G has three steps where in two of them KE decreases (D to E, E to F), and only one where it increases (F to G), so predominantly decrease.

Whereas for b: B to F (KE↓), F to E (KE↑), E to C (KE↓) — two down, one up, same thing.

But in b, from B to F is large increase in height, so large KE decrease, then F to E is decrease in height, KE increase, etc.

I think both could be argued, but let's see what is commonly accepted.

Upon second thought, for question 6, "increase in kinetic energy", option d: A,B,C,D — from A to D, height from 4 to 0, so large increase in KE, and although there is a bump at C, the net effect is increase.

Similarly, for question 7, "decrease in potential energy", option d: G,F,C,D — G3 to F5 (PE↑), F5 to C3 (PE↓), C3 to D0 (PE↓), net from G to D: 3 to 0, decrease of 3, so net decrease.

For question 8, "decrease in kinetic energy", option c: D,E,F,G — D0 to E2 (KE↓), E2 to F5 (KE↓), F5 to G3 (KE↑), net from D to G: 0 to 3, so net KE decrease of 3g, while the increase from F to G is only 2g (from 5 to 3, Δh= -2, so ΔKE= +2g), but the decreases are larger: D to E: Δh=+2, ΔKE= -2g; E to F: Δh=+3, ΔKE= -3g; so total ΔKE = -2 -3 +2 = -3g, so net decrease.

Similarly for b: B to F: Δh=+4, ΔKE= -4g; F to E: Δh= -3, ΔKE= +3g; E to C: Δh=+1, ΔKE= -1g; net ΔKE = -4 +3 -1 = -2g, so also decrease, but smaller magnitude.

But the question doesn't specify magnitude, so both are correct, but perhaps c is better because it has a larger net decrease or is more straightforward.

In many sources, for a similar graph, the answer for 8 is c. D,E,F,G.

So I'll go with that.

So summary for Part 1:

1. D
2. F
3. F
4. D
5. a
6. d (A,B,C,D)
7. d (G,F,C,D)
8. c (D,E,F,G)

Now Part 2: Determine kinetic or potential energy.

Recall:
- Kinetic energy: energy of motion — if the object is moving, it has KE.
- Potential energy: stored energy due to position — if it's at a height, it has gravitational PE.

1. Volleyball served with mass 2.1 kg, speed 30 m/sec — it's moving, so has kinetic energy. Also, if it's in air, it has PE, but the question is to write "kinetic" or "potential" on the line, and hint says you don't have to do math, so probably they want the primary form or the one mentioned.

The sentence is: "You serve a volleyball... The ball leaves your hand with a speed of 30m/sec." So at that instant, it has speed, so kinetic energy. It may also have PE if above ground, but typically in such contexts, when they give speed, they emphasize KE.

The instruction: "Write Kinetic or Potential on the line provided." and for this, it's clearly moving, so kinetic.

2. Baby stroller sitting at top of hill 21m high — not moving, at height, so potential energy.

3. Car traveling with velocity 40 m/sec east, mass 1120 kg — moving, so kinetic energy.

4. Swim meet, first and second place swimmers standing on platform at two different heights. Who has more potential energy? Explain.

Potential energy depends on mass and height: PE = mgh.

Swimmers may have different masses, but typically in such problems, if not specified, we assume same mass, or compare based on height.

The question says "stand on the platform at two different heights", so likely the one at higher height has more PE, assuming same mass.

But it doesn't specify masses, so we have to assume that mass is the same, or that height is the determining factor.

In reality, if one swimmer is heavier, they might have more PE even at lower height, but since no masses given, probably we assume same mass, so higher height means more PE.

The platforms are at different heights, and swimmers are standing, so the one on the higher platform has more gravitational potential energy.

Answer: The swimmer on the higher platform has more potential energy, because potential energy increases with height.

Now to box the answers.

First, Part 1 answers:

1. D
2. F
3. F
4. D
5. a
6. d
7. d
8. c

Part 2:

1. kinetic
2. potential
3. kinetic
4. The swimmer on the higher platform has more potential energy because potential energy depends on height, and the higher the object, the more potential energy it has (assuming similar mass).

For the explanation in 4, keep it simple.

Final Answer format.

Since the user didn't select any options, I'll provide the answers directly.

But according to the response format, I need to have Final Answer section after reasoning.

So let's compile.