A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 68.0000 ft/s; acceleration (a) = 21.0000 ft/s²; distance (s) = 462.0 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) = 68.0000 ft/s, acceleration (a) = 21.0000 ft/s², distance (s) = 462.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 155.0\ \text{ft/s}$$

6. Step 6 — Check: returning v = 155.0 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

• 310.0 — kept a factor of two that cancels in the correct rearrangement.
• 77.5048 — dropped that same factor in the other direction.
• 170.5 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 88.0000 ft/s; distance (s) = 386.0 ft; final velocity (v) = 80.4000 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) = 88.0000 ft/s, distance (s) = 386.0 ft, final velocity (v) = 80.4000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -1.6578\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -1.6578 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

• -3.3156 — kept a factor of two that cancels in the correct rearrangement.
• -0.8289 — dropped that same factor in the other direction.
• -1.8236 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 87.0000 ft/s; acceleration (a) = -10.5000 ft/s²; final velocity (v) = 24.1000 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) = 87.0000 ft/s, acceleration (a) = -10.5000 ft/s², final velocity (v) = 24.1000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 332.8\ \text{ft}$$

6. Step 6 — Check: returning s = 332.8 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

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

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 40.0000 ft/s; acceleration (a) = 15.5000 ft/s²; distance (s) = 157.0 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) = 15.5000 ft/s², distance (s) = 157.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 80.4177\ \text{ft/s}$$

6. Step 6 — Check: returning v = 80.4177 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

• 160.8 — kept a factor of two that cancels in the correct rearrangement.
• 40.2088 — dropped that same factor in the other direction.
• 88.4594 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 14.0000 ft/s; distance (s) = 14.0000 ft; final velocity (v) = 52.0000 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) = 14.0000 ft/s, distance (s) = 14.0000 ft, final velocity (v) = 52.0000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 89.5714\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 89.5714 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

• 179.1 — kept a factor of two that cancels in the correct rearrangement.
• 44.7857 — dropped that same factor in the other direction.
• 98.5286 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 39.0000 ft/s; acceleration (a) = 23.0000 ft/s²; final velocity (v) = 99.7000 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) = 39.0000 ft/s, acceleration (a) = 23.0000 ft/s², final velocity (v) = 99.7000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 183.0\ \text{ft}$$

6. Step 6 — Check: returning s = 183.0 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

• 366.0 — kept a factor of two that cancels in the correct rearrangement.
• 91.5118 — dropped that same factor in the other direction.
• 201.3 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 34.0000 ft/s; acceleration (a) = 22.0000 ft/s²; distance (s) = 141.0 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) = 34.0000 ft/s, acceleration (a) = 22.0000 ft/s², distance (s) = 141.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 85.7904\ \text{ft/s}$$

6. Step 6 — Check: returning v = 85.7904 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

• 171.6 — kept a factor of two that cancels in the correct rearrangement.
• 42.8952 — dropped that same factor in the other direction.
• 94.3695 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 58.0000 ft/s; distance (s) = 474.0 ft; final velocity (v) = 53.4000 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) = 58.0000 ft/s, distance (s) = 474.0 ft, final velocity (v) = 53.4000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -0.5405\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -0.5405 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

• -1.0811 — kept a factor of two that cancels in the correct rearrangement.
• -0.2703 — dropped that same factor in the other direction.
• -0.5946 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 66.0000 ft/s; acceleration (a) = -25.5000 ft/s²; final velocity (v) = 42.1000 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) = 66.0000 ft/s, acceleration (a) = -25.5000 ft/s², final velocity (v) = 42.1000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 50.6586\ \text{ft}$$

6. Step 6 — Check: returning s = 50.6586 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

• 101.3 — kept a factor of two that cancels in the correct rearrangement.
• 25.3293 — dropped that same factor in the other direction.
• 55.7245 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 75.0000 ft/s; acceleration (a) = -20.5000 ft/s²; distance (s) = 32.0000 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) = 75.0000 ft/s, acceleration (a) = -20.5000 ft/s², distance (s) = 32.0000 ft.

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

5. Step 5 — Evaluate:

   $$v = 65.6734\ \text{ft/s}$$

6. Step 6 — Check: returning v = 65.6734 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

• 131.3 — kept a factor of two that cancels in the correct rearrangement.
• 32.8367 — dropped that same factor in the other direction.
• 72.2408 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Translating Axes x-y