A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 64.0000 ft/s; acceleration (a) = 8.5000 ft/s²; distance (s) = 208.0 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) = 64.0000 ft/s, acceleration (a) = 8.5000 ft/s², distance (s) = 208.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 87.3613\ \text{ft/s}$$

6. Step 6 — Check: returning v = 87.3613 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

• 174.7 — kept a factor of two that cancels in the correct rearrangement.
• 43.6807 — dropped that same factor in the other direction.
• 96.0975 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 68.0000 ft/s; distance (s) = 127.0 ft; final velocity (v) = 63.1000 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) = 68.0000 ft/s, distance (s) = 127.0 ft, final velocity (v) = 63.1000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -2.5291\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -2.5291 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

• -5.0582 — kept a factor of two that cancels in the correct rearrangement.
• -1.2645 — dropped that same factor in the other direction.
• -2.7820 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 95.0000 ft/s; acceleration (a) = -13.0000 ft/s²; final velocity (v) = 78.0000 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) = 95.0000 ft/s, acceleration (a) = -13.0000 ft/s², final velocity (v) = 78.0000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 113.1\ \text{ft}$$

6. Step 6 — Check: returning s = 113.1 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

• 226.2 — kept a factor of two that cancels in the correct rearrangement.
• 56.5577 — dropped that same factor in the other direction.
• 124.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 38.0000 ft/s; acceleration (a) = -15.5000 ft/s²; distance (s) = 182.0 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) = 38.0000 ft/s, acceleration (a) = -15.5000 ft/s², distance (s) = 182.0 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 → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 20.0000 ft/s; distance (s) = 133.0 ft; final velocity (v) = 76.6000 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) = 20.0000 ft/s, distance (s) = 133.0 ft, final velocity (v) = 76.6000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 20.5547\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 20.5547 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

• 41.1095 — kept a factor of two that cancels in the correct rearrangement.
• 10.2774 — dropped that same factor in the other direction.
• 22.6102 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 26.0000 ft/s; acceleration (a) = 14.0000 ft/s²; final velocity (v) = 47.4000 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) = 26.0000 ft/s, acceleration (a) = 14.0000 ft/s², final velocity (v) = 47.4000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 56.0986\ \text{ft}$$

6. Step 6 — Check: returning s = 56.0986 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

• 112.2 — kept a factor of two that cancels in the correct rearrangement.
• 28.0493 — dropped that same factor in the other direction.
• 61.7084 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 40.0000 ft/s; acceleration (a) = 23.0000 ft/s²; distance (s) = 459.0 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) = 40.0000 ft/s, acceleration (a) = 23.0000 ft/s², distance (s) = 459.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 150.7\ \text{ft/s}$$

6. Step 6 — Check: returning v = 150.7 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

• 301.4 — kept a factor of two that cancels in the correct rearrangement.
• 75.3558 — dropped that same factor in the other direction.
• 165.8 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 59.0000 ft/s; distance (s) = 418.0 ft; final velocity (v) = 145.1 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) = 59.0000 ft/s, distance (s) = 418.0 ft, final velocity (v) = 145.1 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 21.0203\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 21.0203 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

• 42.0407 — kept a factor of two that cancels in the correct rearrangement.
• 10.5102 — dropped that same factor in the other direction.
• 23.1224 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 95.0000 ft/s; acceleration (a) = -9.0000 ft/s²; final velocity (v) = 23.7000 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) = 95.0000 ft/s, acceleration (a) = -9.0000 ft/s², final velocity (v) = 23.7000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 470.2\ \text{ft}$$

6. Step 6 — Check: returning s = 470.2 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

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

Reference: FE Reference Handbook — Dynamics → Newton's second law for a particle is

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 54.0000 ft/s; acceleration (a) = -4.0000 ft/s²; distance (s) = 440.0 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) = 54.0000 ft/s, acceleration (a) = -4.0000 ft/s², distance (s) = 440.0 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 → Newton's second law for a particle is