A dynamics problem uses Work–energy theorem. Given mass (m) = 300.0 kg; initial speed (v1) = 15.0000 m/s; final speed (v2) = 21.0000 m/s, determine the work done (W) in J.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except W is given, so isolate W symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that W stands alone on the left-hand side.

3. Step 3 — List the givens: mass (m) = 300.0 kg, initial speed (v1) = 15.0000 m/s, final speed (v2) = 21.0000 m/s.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$W = 32400\ \text{J}$$

6. Step 6 — Check: returning W = 32,400 J to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 64,800 — kept a factor of two that cancels in the correct rearrangement.
• 16,200 — dropped that same factor in the other direction.
• 35,640 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given initial speed (v1) = 3.0000 m/s; final speed (v2) = 24.5000 m/s; work done (W) = 308,420 J, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3 — List the givens: initial speed (v1) = 3.0000 m/s, final speed (v2) = 24.5000 m/s, work done (W) = 308,420 J.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = 1043\ \text{kg}$$

6. Step 6 — Check: returning m = 1,043 kg to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,087 — kept a factor of two that cancels in the correct rearrangement.
• 521.6 — dropped that same factor in the other direction.
• 1,148 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given mass (m) = 1,750 kg; initial speed (v1) = 5.5000 m/s; final speed (v2) = 38.5000 m/s, determine the work done (W) in J.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except W is given, so isolate W symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that W stands alone on the left-hand side.

3. Step 3 — List the givens: mass (m) = 1,750 kg, initial speed (v1) = 5.5000 m/s, final speed (v2) = 38.5000 m/s.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$W = 1270500\ \text{J}$$

6. Step 6 — Check: returning W = 1,270,500 J to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,541,000 — kept a factor of two that cancels in the correct rearrangement.
• 635,250 — dropped that same factor in the other direction.
• 1,397,550 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given initial speed (v1) = 5.0000 m/s; final speed (v2) = 39.5000 m/s; work done (W) = 103,335 J, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3 — List the givens: initial speed (v1) = 5.0000 m/s, final speed (v2) = 39.5000 m/s, work done (W) = 103,335 J.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = 134.6\ \text{kg}$$

6. Step 6 — Check: returning m = 134.6 kg to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 269.2 — kept a factor of two that cancels in the correct rearrangement.
• 67.3083 — dropped that same factor in the other direction.
• 148.1 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given mass (m) = 1,740 kg; initial speed (v1) = 1.5000 m/s; final speed (v2) = 17.5000 m/s, determine the work done (W) in J.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except W is given, so isolate W symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that W stands alone on the left-hand side.

3. Step 3 — List the givens: mass (m) = 1,740 kg, initial speed (v1) = 1.5000 m/s, final speed (v2) = 17.5000 m/s.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$W = 264480\ \text{J}$$

6. Step 6 — Check: returning W = 264,480 J to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 528,960 — kept a factor of two that cancels in the correct rearrangement.
• 132,240 — dropped that same factor in the other direction.
• 290,928 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given initial speed (v1) = 15.0000 m/s; final speed (v2) = 9.0000 m/s; work done (W) = 1,523,930 J, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3 — List the givens: initial speed (v1) = 15.0000 m/s, final speed (v2) = 9.0000 m/s, work done (W) = 1,523,930 J.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = -21166\ \text{kg}$$

6. Step 6 — Check: returning m = -21,166 kg to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -42,331 — kept a factor of two that cancels in the correct rearrangement.
• -10,583 — dropped that same factor in the other direction.
• -23,282 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given mass (m) = 1,040 kg; initial speed (v1) = 8.0000 m/s; final speed (v2) = 10.5000 m/s, determine the work done (W) in J.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except W is given, so isolate W symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that W stands alone on the left-hand side.

3. Step 3 — List the givens: mass (m) = 1,040 kg, initial speed (v1) = 8.0000 m/s, final speed (v2) = 10.5000 m/s.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$W = 24050\ \text{J}$$

6. Step 6 — Check: returning W = 24,050 J to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 48,100 — kept a factor of two that cancels in the correct rearrangement.
• 12,025 — dropped that same factor in the other direction.
• 26,455 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given initial speed (v1) = 8.5000 m/s; final speed (v2) = 16.5000 m/s; work done (W) = 218,712 J, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3 — List the givens: initial speed (v1) = 8.5000 m/s, final speed (v2) = 16.5000 m/s, work done (W) = 218,712 J.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = 2187\ \text{kg}$$

6. Step 6 — Check: returning m = 2,187 kg to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4,374 — kept a factor of two that cancels in the correct rearrangement.
• 1,094 — dropped that same factor in the other direction.
• 2,406 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given mass (m) = 1,640 kg; initial speed (v1) = 3.5000 m/s; final speed (v2) = 25.0000 m/s, determine the work done (W) in J.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except W is given, so isolate W symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that W stands alone on the left-hand side.

3. Step 3 — List the givens: mass (m) = 1,640 kg, initial speed (v1) = 3.5000 m/s, final speed (v2) = 25.0000 m/s.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$W = 502455\ \text{J}$$

6. Step 6 — Check: returning W = 502,455 J to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,004,910 — kept a factor of two that cancels in the correct rearrangement.
• 251,228 — dropped that same factor in the other direction.
• 552,701 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as

A dynamics problem uses Work–energy theorem. Given initial speed (v1) = 17.0000 m/s; final speed (v2) = 6.5000 m/s; work done (W) = 1,891,161 J, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Work–energy theorem.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

2. Step 2 — Rearrange the relation so that m stands alone on the left-hand side.

3. Step 3 — List the givens: initial speed (v1) = 17.0000 m/s, final speed (v2) = 6.5000 m/s, work done (W) = 1,891,161 J.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$m = -15329\ \text{kg}$$

6. Step 6 — Check: returning m = -15,329 kg to

   $$W = \tfrac12 m (v_2^2 - v_1^2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -30,657 — kept a factor of two that cancels in the correct rearrangement.
• -7,664 — dropped that same factor in the other direction.
• -16,861 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Work U is defined as