A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 53.0000 ft/s; acceleration (a) = -16.5000 ft/s²; distance (s) = 306.0 ft, determine the final velocity (v) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except v is given, so isolate v 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 53.0000 ft/s, acceleration (a) = -16.5000 ft/s², distance (s) = 306.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 0.0000\ \text{ft/s}$$

6. Step 6 — Check: returning v = 0.0000 ft/s to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 0.0000 — kept a factor of two that cancels in the correct rearrangement.
• 0.0000 — dropped that same factor in the other direction.
• 0.0000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 98.0000 ft/s; distance (s) = 398.0 ft; final velocity (v) = 119.2 ft/s, determine the acceleration (a) in ft/s².

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except a is given, so isolate a 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 98.0000 ft/s, distance (s) = 398.0 ft, final velocity (v) = 119.2 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 5.7847\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 5.7847 ft/s² to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 11.5694 — kept a factor of two that cancels in the correct rearrangement.
• 2.8924 — dropped that same factor in the other direction.
• 6.3632 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 37.0000 ft/s; acceleration (a) = 16.5000 ft/s²; final velocity (v) = 101.2 ft/s, determine the distance (s) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except s is given, so isolate s 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 37.0000 ft/s, acceleration (a) = 16.5000 ft/s², final velocity (v) = 101.2 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 268.9\ \text{ft}$$

6. Step 6 — Check: returning s = 268.9 ft to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 77.0000 ft/s; acceleration (a) = -1.0000 ft/s²; distance (s) = 73.0000 ft, determine the final velocity (v) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except v is given, so isolate v 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 77.0000 ft/s, acceleration (a) = -1.0000 ft/s², distance (s) = 73.0000 ft.

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

5. Step 5 — Evaluate:

   $$v = 76.0460\ \text{ft/s}$$

6. Step 6 — Check: returning v = 76.0460 ft/s to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 152.1 — kept a factor of two that cancels in the correct rearrangement.
• 38.0230 — dropped that same factor in the other direction.
• 83.6506 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 39.0000 ft/s; distance (s) = 158.0 ft; final velocity (v) = 79.8000 ft/s, determine the acceleration (a) in ft/s².

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except a is given, so isolate a 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 39.0000 ft/s, distance (s) = 158.0 ft, final velocity (v) = 79.8000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 15.3387\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 15.3387 ft/s² to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 30.6775 — kept a factor of two that cancels in the correct rearrangement.
• 7.6694 — dropped that same factor in the other direction.
• 16.8726 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 94.0000 ft/s; acceleration (a) = -2.5000 ft/s²; final velocity (v) = 13.8000 ft/s, determine the distance (s) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except s is given, so isolate s 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 94.0000 ft/s, acceleration (a) = -2.5000 ft/s², final velocity (v) = 13.8000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 1729\ \text{ft}$$

6. Step 6 — Check: returning s = 1,729 ft to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 3,458 — kept a factor of two that cancels in the correct rearrangement.
• 864.6 — dropped that same factor in the other direction.
• 1,902 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 96.0000 ft/s; acceleration (a) = 21.0000 ft/s²; distance (s) = 90.0000 ft, determine the final velocity (v) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except v is given, so isolate v 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 96.0000 ft/s, acceleration (a) = 21.0000 ft/s², distance (s) = 90.0000 ft.

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

5. Step 5 — Evaluate:

   $$v = 114.0\ \text{ft/s}$$

6. Step 6 — Check: returning v = 114.0 ft/s to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 228.0 — kept a factor of two that cancels in the correct rearrangement.
• 57.0000 — dropped that same factor in the other direction.
• 125.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 54.0000 ft/s; distance (s) = 166.0 ft; final velocity (v) = 18.9000 ft/s, determine the acceleration (a) in ft/s².

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except a is given, so isolate a 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 54.0000 ft/s, distance (s) = 166.0 ft, final velocity (v) = 18.9000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -7.7072\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -7.7072 ft/s² to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• -15.4144 — kept a factor of two that cancels in the correct rearrangement.
• -3.8536 — dropped that same factor in the other direction.
• -8.4779 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 84.0000 ft/s; acceleration (a) = 12.0000 ft/s²; final velocity (v) = 100.6 ft/s, determine the distance (s) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except s is given, so isolate s 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 84.0000 ft/s, acceleration (a) = 12.0000 ft/s², final velocity (v) = 100.6 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 127.7\ \text{ft}$$

6. Step 6 — Check: returning s = 127.7 ft to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 255.4 — kept a factor of two that cancels in the correct rearrangement.
• 63.8408 — dropped that same factor in the other direction.
• 140.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 87.0000 ft/s; acceleration (a) = -19.0000 ft/s²; distance (s) = 397.0 ft, determine the final velocity (v) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant-acceleration kinematics.
• Everything except v is given, so isolate v 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:

   $$v^2 = v_0^2 + 2 a s$$

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

3. Step 3 — List the givens: initial velocity (v0) = 87.0000 ft/s, acceleration (a) = -19.0000 ft/s², distance (s) = 397.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 0.0000\ \text{ft/s}$$

6. Step 6 — Check: returning v = 0.0000 ft/s to

   $$v^2 = v_0^2 + 2 a s$$

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

Why the other options are there

• 0.0000 — kept a factor of two that cancels in the correct rearrangement.
• 0.0000 — dropped that same factor in the other direction.
• 0.0000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Concept of Weight