A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 64.0000 ft/s; acceleration (a) = -21.0000 ft/s²; distance (s) = 469.0 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) = -21.0000 ft/s², distance (s) = 469.0 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 → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 76.0000 ft/s; distance (s) = 420.0 ft; final velocity (v) = 73.2000 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) = 76.0000 ft/s, distance (s) = 420.0 ft, final velocity (v) = 73.2000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -0.4973\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -0.4973 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

• -0.9947 — kept a factor of two that cancels in the correct rearrangement.
• -0.2487 — dropped that same factor in the other direction.
• -0.5471 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 48.0000 ft/s; acceleration (a) = -18.0000 ft/s²; final velocity (v) = 52.4000 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) = 48.0000 ft/s, acceleration (a) = -18.0000 ft/s², final velocity (v) = 52.4000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = -12.2711\ \text{ft}$$

6. Step 6 — Check: returning s = -12.2711 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

• -24.5422 — kept a factor of two that cancels in the correct rearrangement.
• -6.1356 — dropped that same factor in the other direction.
• -13.4982 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 73.0000 ft/s; acceleration (a) = -19.0000 ft/s²; distance (s) = 50.0000 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) = 73.0000 ft/s, acceleration (a) = -19.0000 ft/s², distance (s) = 50.0000 ft.

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

5. Step 5 — Evaluate:

   $$v = 58.5577\ \text{ft/s}$$

6. Step 6 — Check: returning v = 58.5577 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

• 117.1 — kept a factor of two that cancels in the correct rearrangement.
• 29.2788 — dropped that same factor in the other direction.
• 64.4134 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 61.0000 ft/s; distance (s) = 231.0 ft; final velocity (v) = 14.1000 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) = 61.0000 ft/s, distance (s) = 231.0 ft, final velocity (v) = 14.1000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -7.6238\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -7.6238 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

• -15.2476 — kept a factor of two that cancels in the correct rearrangement.
• -3.8119 — dropped that same factor in the other direction.
• -8.3862 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 42.0000 ft/s; acceleration (a) = 25.5000 ft/s²; final velocity (v) = 86.1000 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) = 42.0000 ft/s, acceleration (a) = 25.5000 ft/s², final velocity (v) = 86.1000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 110.8\ \text{ft}$$

6. Step 6 — Check: returning s = 110.8 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

• 221.5 — kept a factor of two that cancels in the correct rearrangement.
• 55.3844 — dropped that same factor in the other direction.
• 121.8 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 78.0000 ft/s; acceleration (a) = 10.0000 ft/s²; distance (s) = 277.0 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) = 78.0000 ft/s, acceleration (a) = 10.0000 ft/s², distance (s) = 277.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 107.8\ \text{ft/s}$$

6. Step 6 — Check: returning v = 107.8 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

• 215.6 — kept a factor of two that cancels in the correct rearrangement.
• 53.9073 — dropped that same factor in the other direction.
• 118.6 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 84.0000 ft/s; distance (s) = 298.0 ft; final velocity (v) = 146.8 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) = 84.0000 ft/s, distance (s) = 298.0 ft, final velocity (v) = 146.8 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 24.3192\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 24.3192 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

• 48.6384 — kept a factor of two that cancels in the correct rearrangement.
• 12.1596 — dropped that same factor in the other direction.
• 26.7511 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 10.0000 ft/s; acceleration (a) = 3.0000 ft/s²; final velocity (v) = 46.0000 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) = 10.0000 ft/s, acceleration (a) = 3.0000 ft/s², final velocity (v) = 46.0000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 336.0\ \text{ft}$$

6. Step 6 — Check: returning s = 336.0 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

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

Reference: FE Reference Handbook — Dynamics → Common Nomenclature

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 89.0000 ft/s; acceleration (a) = 12.0000 ft/s²; distance (s) = 464.0 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) = 89.0000 ft/s, acceleration (a) = 12.0000 ft/s², distance (s) = 464.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 138.0\ \text{ft/s}$$

6. Step 6 — Check: returning v = 138.0 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

• 276.1 — kept a factor of two that cancels in the correct rearrangement.
• 69.0235 — dropped that same factor in the other direction.
• 151.9 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Common Nomenclature