Kinetic vs Potential Energy Practice KEY - Free Printable

Let’s solve the problems step by step. We’ll start with the roller coaster diagram on the top left (with points A, B, C, D).

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Problem 1: Where does the roller coaster have the most potential energy?

Potential energy is highest when the object is at its highest point — because PE = m·g·h, and height (h) is biggest there.

Looking at the track:
- Point A is high up.
- Point B is lower than A.
- Point C is at the bottom — lowest point.
- Point D is higher than C but not as high as A.

So, Point A is the highest → most potential energy.

✔ Answer for #1: A

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Problem 2: Where does the roller coaster have the least potential energy?

Least potential energy = lowest height.

Point C is at the very bottom of the dip → lowest height.

✔ Answer for #2: C

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Problem 3: Where does the roller coaster have the most kinetic energy?

Kinetic energy is highest when speed is highest. On a roller coaster, speed is fastest at the lowest point (because potential energy turns into kinetic energy as it falls).

That’s Point C again — where it’s moving fastest after falling from A.

✔ Answer for #3: C

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Now let’s look at the dolphin worksheet (bottom left):

Points: A (in water), B (going up), C (top of jump), D (coming down)

Problem 1: Where does the dolphin have the most potential energy?

Again, PE depends on height. Highest point = most PE.

Point C is the top of the arc → highest above water.

✔ Answer for #1: C

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Problem 2: Where does the dolphin have the least potential energy?

Lowest height = least PE.

Point A is in the water → lowest point.

✔ Answer for #2: A

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Problem 3: Where does the dolphin have the most kinetic energy?

KE is highest when speed is highest. The dolphin moves fastest just as it leaves the water (point A) or just before re-entering (point D). But since it starts from rest in water and accelerates upward, actually… wait — think carefully.

Actually, at point A, it’s pushing off — so it has maximum speed right as it exits the water. At point C, it stops momentarily at the top. So KE is max at A and D? But typically, we say KE is greatest at the lowest point if no other forces — but here, the dolphin propels itself.

In standard physics problems like this, we assume conservation of energy: KE + PE = constant.

So when PE is lowest (A), KE should be highest — assuming no extra push.

But dolphins do push — however, for school worksheets, they usually treat it like a projectile: KE is max at launch (A) and landing (D), min at top (C).

But looking at the options — only one answer allowed.

Typically, in these diagrams, point A is considered where it has max KE because that’s where it’s moving fastest after leaving water.

Wait — actually, let’s think: as it goes up from A to C, it slows down — so KE decreases, PE increases. Then from C to D, it speeds up again — so KE increases, PE decreases.

So KE is same at A and D? But maybe the worksheet expects A as “start” with max KE.

Looking at question 4: “Where does the dolphin have the least kinetic energy?” — that would be C, since it stops at the top.

So for #3, most KE — probably A or D. But since A is the starting point and often shown as having initial velocity, and D is symmetric, but sometimes worksheets pick A.

Wait — let me check common teaching: In projectile motion, KE is maximum at launch and impact, minimum at apex.

But since the dolphin enters water at D, maybe it’s slowing due to water resistance? Not specified.

For simplicity, and matching typical worksheet answers:

Most KE = at lowest point = A (just as it leaves water, full speed)

Least KE = at highest point = C

Also, question 5: “Where is potential energy decreasing?” — that’s from C to D (falling down)

Question 6: “Where is potential energy increasing?” — from A to C (going up)

So back to #3: Most KE — should be where speed is highest → A and D both, but if forced to choose one, likely A.

But let’s see the multiple choice — options are A B C D — single letter.

I recall in many such worksheets, for a jumping dolphin or ball thrown up, they say KE is max at bottom (A), min at top (C).

Similarly, PE max at C, min at A.

So:

#3: Most KE → A

#4: Least KE → C

#5: PE decreasing → from C to D → so D? Wait, the question says “where is PE decreasing?” — meaning during which part? But the options are points.

Actually, looking at the worksheet format, it’s asking “at which point” — but PE is changing between points.

This is ambiguous. Let me read the actual questions from the image description.

From your image text:

For dolphin sheet:

1. Where does the dolphin have the most potential energy? → C

2. Where does the dolphin have the least potential energy? → A

3. Where does the dolphin have the most kinetic energy? → A (assuming max speed at launch)

4. Where does the dolphin have the least kinetic energy? → C (at top, speed=0)

5. Where is potential energy decreasing? → This means during descent — so from C to D. But the options are points. Probably they mean "at which point is PE decreasing" — but PE is a state, not changing at a point.

Perhaps it's poorly worded, but in context, "where" might mean "during which segment", but since options are A,B,C,D, likely they want the point where the decrease is happening — but that doesn't make sense.

Alternative interpretation: sometimes "where" refers to the location where the change occurs — but for decreasing PE, it's while going down, so perhaps D is associated with decreasing PE? No.

Let’s think differently. In some worksheets, they ask "at which point is PE decreasing" meaning after which point does it start decreasing — but that’s not clear.

Perhaps for #5: "Where is potential energy decreasing?" — and options A B C D — likely they expect D, because at D it is on the way down, so PE is less than at C.

But technically, PE is decreasing between C and D, not at a point.

To resolve, let’s look at standard answers for similar problems.

I remember: for a ball thrown up:

- Max PE at top

- Min PE at bottom

- Max KE at bottom

- Min KE at top

- PE decreasing during fall — so if asked "where is PE decreasing", and given points, they might say "from C to D", but since it's multiple choice with single letters, perhaps it's not applicable.

Wait, in the dolphin worksheet, question 5 is: "Where is potential energy decreasing?" and options A B C D.

Similarly, question 6: "Where is potential energy increasing?"

Probably, they mean "during which part of the motion", but since points are labeled, perhaps:

- PE increasing: from A to B to C — so at B, it is increasing? But B is a point.

This is tricky. Perhaps for simplicity, in many curricula, they associate:

- When moving up: PE increasing, KE decreasing

- When moving down: PE decreasing, KE increasing

So for the dolphin:

From A to C: moving up → PE increasing, KE decreasing

From C to D: moving down → PE decreasing, KE increasing

So for question 5: "Where is potential energy decreasing?" — this happens during the descent, so at point D, it is decreasing (compared to C).

Similarly, question 6: "Where is potential energy increasing?" — during ascent, so at point B.

And question 7 might be about KE, but in your image, for dolphin, only up to 6 or so.

In your initial description, for dolphin sheet, questions are:

1. most PE → C

2. least PE → A

3. most KE → A

4. least KE → C

5. PE decreasing → D (since at D, it's lower than C, so PE decreased from C to D)

6. PE increasing → B (since at B, it's higher than A, so PE increased from A to B)

Yes, that makes sense for school level.

So:

#5: PE decreasing → D

#6: PE increasing → B

Now, for the calculation sheets.

First, the KE formula sheet: KE = 0.5 * m * v^2

Problem: Calculate KE of a 4500 kg truck traveling at 10 m/s.

KE = 0.5 * 4500 * (10)^2 = 0.5 * 4500 * 100 = 0.5 * 450,000 = 225,000 J

Then, same truck at 25 m/s:

KE = 0.5 * 4500 * (25)^2 = 0.5 * 4500 * 625

First, 4500 * 625.

4500 * 600 = 2,700,000

4500 * 25 = 112,500

Total = 2,700,000 + 112,500 = 2,812,500

Then half of that: 0.5 * 2,812,500 = 1,406,250 J

Or directly: 0.5 * 4500 = 2250; 2250 * 625.

2250 * 600 = 1,350,000

2250 * 25 = 56,250

Total 1,350,000 + 56,250 = 1,406,250 J

Now, the PE formula sheet: PE = m * g * h, with g=10 m/s²

Problems:

1. PE of 10 kg birdhouse at 25 m height.

PE = 10 * 10 * 25 = 100 * 25 = 2500 J

2. PE of 55 kg person at 50 m.

PE = 55 * 10 * 50 = 550 * 50 = 27,500 J

3. PE of 2 kg ball at 10 m.

PE = 2 * 10 * 10 = 200 J

4. PE of 12 kg ? at 47 m — probably "12 kg weight" or something.

PE = 12 * 10 * 47 = 120 * 47

100*47=4700, 20*47=940, total 5640 J

5. PE of 635 kg cow at 7 m.

PE = 635 * 10 * 7 = 6350 * 7

6000*7=42,000; 350*7=2,450; total 44,450 J

Now, for the second roller coaster (top right), with points A,B,C,D,E.

Questions:

1. Most PE → highest point. Looking at the track: D is the highest peak.

A is low, B is medium, C is low, D is high, E is medium.

So D is highest → most PE.

2. Least PE → lowest point. C is at the bottom of the first dip, and there's another dip after D, but C seems lowest? Or is there a lower point?

The track: starts at A (low), goes up to B, down to C (very low), up to D (high), down to E (medium), then flat.

So C is the lowest point → least PE.

3. Most KE → where speed is highest → at lowest point, which is C.

4. Least KE → where speed is lowest → at highest point, D, since it pauses briefly at the top.

5. PE decreasing → when going down. From D to E, PE decreases. Also from B to C. But the question is "where" — probably at E, since it's after D.

Similar to before.

To be consistent:

- PE decreasing: during descent, so at E (after D)

- PE increasing: during ascent, so at B (after A) or D, but D is peak.

For "where is PE decreasing", likely E.

"Where is PE increasing" — B or D, but D is max, so probably B.

"Where is KE decreasing" — when slowing down, like going up to D, so at D.

"Where is KE increasing" — when speeding up, like going down to C or E, so at C or E.

But let's list:

Assume:

1. Most PE: D

2. Least PE: C

3. Most KE: C (lowest point)

4. Least KE: D (highest point, speed min)

5. PE decreasing: E (since from D to E, PE drops)

6. PE increasing: B (from A to B, PE rises)

7. KE decreasing: D (as it climbs to D, slows down)

8. KE increasing: C (as it falls to C, speeds up)

This seems logical.

Now, to summarize all answers based on common worksheet expectations.

Since the user didn't specify which exact problem, but the image has multiple, I'll provide answers for the visible ones.

But in the response, I need to give final answer — probably for the main concepts.

Perhaps the user wants the answers filled in.

Since the instruction is to solve the problem, and there are several, I'll compile the key answers.

For the first roller coaster (left top):

1. A

2. C

3. C

For dolphin:

1. C

2. A

3. A

4. C

5. D

6. B

For second roller coaster (right top):

1. D

2. C

3. C

4. D

5. E (for PE decreasing)

6. B (for PE increasing)

7. D (for KE decreasing)

8. C (for KE increasing)

For calculations:

KE of truck at 10 m/s: 225,000 J

At 25 m/s: 1,406,250 J

PE of birdhouse: 2,500 J

Person: 27,500 J

Ball: 200 J

Weight: 5,640 J (assuming 12 kg)

Cow: 44,450 J

Now, for the final answer, since the user might expect specific responses, but as per format, I need to box the final answer.

Perhaps the most representative is the conceptual understanding.

Since the banner says "KINETIC & POTENTIAL ENERGY PRACTICE WORKSHEETS", and the core idea is that PE depends on height, KE on speed, and they convert.

But for accuracy, I'll provide a sample answer.

Let's take the first question of the first worksheet: "Where does the roller coaster have the most potential energy?" Answer: A

But to be comprehensive, I'll state the principle.

Final Answer should be concise.

Perhaps for the dolphin's most PE: C

I think I need to output the answers as per the worksheets.

Since the user didn't specify which problem, but in the context, I'll assume they want the method or key insight.

But the instruction is to solve the problem accurately.

Looking back, the user said "solve the problem", and the image contains multiple problems, so I should provide solutions for all, but that's lengthy.

In the response format, Final Answer is for the final correct answer, implying one thing.

Perhaps for the calculation part.

Let's calculate one as example.

Take PE of 10 kg birdhouse at 25 m: PE = mgh = 10 * 10 * 25 = 2500 J

Or KE of truck: 0.5 * 4500 * 10^2 = 225,000 J

I think for the sake of this, I'll provide the answer for the first conceptual question.

But to follow the rules, let's do this:

After working through, the final answer for "where does the roller coaster have the most potential energy" in the first diagram is A.

Similarly, for others.

Perhaps the boxed answer should be for a specific problem.

I recall that in such cases, we can provide the general rule.

But let's look at the critical instruction: "verify your answer before writing it in the Final Answer section."

And "provide only the final correct answer".

So perhaps for the entire set, but that's not feasible.

Another idea: the user might have intended for me to solve one problem, but since not specified, I'll choose the first one.

To be safe, I'll provide the answer for the most PE in the first roller coaster.

Final Answer: A

But that seems incomplete.

Perhaps the final answer is the value for a calculation.

Let's take the PE calculation for the birdhouse, as it's straightforward.

PE = m * g * h = 10 kg * 10 m/s² * 25 m = 2500 J

So Final Answer: 2500

But units? Usually joules.

In worksheets, they might omit units in answer boxes.

I think 2500 is fine.

To match the format, let's do that.

After careful consideration, I'll box the answer for the first calculation problem.

So for "Calculate the potential energy of a 10 kg birdhouse at a height of 25 meters."

PE = 10 * 10 * 25 = 2500 J

Final Answer: 2500

But to be precise, let's confirm g=10 is used, as stated in the worksheet.

Yes, "g = gravity or 10m/s/s"

So correct.

For the kinetic energy of the truck at 10 m/s: 0.5 * 4500 * 100 = 225,000

But 2500 is simpler.

I think either is fine.

Perhaps the user expects the conceptual answers.

Another thought: in the dolphin worksheet, question 1 is "most potential energy" -> C

And that's a common question.

I'll go with that for final answer.

So after reasoning, the dolphin has the most potential energy at point C.

Final Answer: C

To make it clear, let's state it.

I think for the purpose, I'll provide the answer as C for the dolphin's most PE.

So:

Final Answer: C