A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 79.0000 ft/s; acceleration (a) = -13.0000 ft/s²; distance (s) = 151.0 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) = 79.0000 ft/s, acceleration (a) = -13.0000 ft/s², distance (s) = 151.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 48.1144\ \text{ft/s}$$

6. Step 6 — Check: returning v = 48.1144 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

• 96.2289 — kept a factor of two that cancels in the correct rearrangement.
• 24.0572 — dropped that same factor in the other direction.
• 52.9259 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 62.0000 ft/s; distance (s) = 451.0 ft; final velocity (v) = 36.6000 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) = 62.0000 ft/s, distance (s) = 451.0 ft, final velocity (v) = 36.6000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -2.7765\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -2.7765 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

• -5.5531 — kept a factor of two that cancels in the correct rearrangement.
• -1.3883 — dropped that same factor in the other direction.
• -3.0542 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 68.0000 ft/s; acceleration (a) = -14.5000 ft/s²; final velocity (v) = 110.9 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) = 68.0000 ft/s, acceleration (a) = -14.5000 ft/s², final velocity (v) = 110.9 ft/s.

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

5. Step 5 — Evaluate:

   $$s = -264.6\ \text{ft}$$

6. Step 6 — Check: returning s = -264.6 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

• -529.3 — kept a factor of two that cancels in the correct rearrangement.
• -132.3 — dropped that same factor in the other direction.
• -291.1 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 25.0000 ft/s; acceleration (a) = -18.5000 ft/s²; distance (s) = 117.0 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) = 25.0000 ft/s, acceleration (a) = -18.5000 ft/s², distance (s) = 117.0 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 → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 13.0000 ft/s; distance (s) = 172.0 ft; final velocity (v) = 7.5000 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) = 13.0000 ft/s, distance (s) = 172.0 ft, final velocity (v) = 7.5000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -0.3278\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -0.3278 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

• -0.6555 — kept a factor of two that cancels in the correct rearrangement.
• -0.1639 — dropped that same factor in the other direction.
• -0.3605 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 71.0000 ft/s; acceleration (a) = 2.5000 ft/s²; final velocity (v) = 98.4000 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) = 71.0000 ft/s, acceleration (a) = 2.5000 ft/s², final velocity (v) = 98.4000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 928.3\ \text{ft}$$

6. Step 6 — Check: returning s = 928.3 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

• 1,857 — kept a factor of two that cancels in the correct rearrangement.
• 464.2 — dropped that same factor in the other direction.
• 1,021 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 64.0000 ft/s; acceleration (a) = -5.5000 ft/s²; distance (s) = 115.0 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) = -5.5000 ft/s², distance (s) = 115.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 53.2071\ \text{ft/s}$$

6. Step 6 — Check: returning v = 53.2071 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

• 106.4 — kept a factor of two that cancels in the correct rearrangement.
• 26.6036 — dropped that same factor in the other direction.
• 58.5279 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 42.0000 ft/s; distance (s) = 434.0 ft; final velocity (v) = 82.5000 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) = 42.0000 ft/s, distance (s) = 434.0 ft, final velocity (v) = 82.5000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 5.8090\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 5.8090 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

• 11.6181 — kept a factor of two that cancels in the correct rearrangement.
• 2.9045 — dropped that same factor in the other direction.
• 6.3899 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 85.0000 ft/s; acceleration (a) = -28.5000 ft/s²; final velocity (v) = 36.7000 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) = 85.0000 ft/s, acceleration (a) = -28.5000 ft/s², final velocity (v) = 36.7000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 103.1\ \text{ft}$$

6. Step 6 — Check: returning s = 103.1 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

• 206.2 — kept a factor of two that cancels in the correct rearrangement.
• 51.5624 — dropped that same factor in the other direction.
• 113.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Particle Rectilinear Motion

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 26.0000 ft/s; acceleration (a) = -27.5000 ft/s²; distance (s) = 465.0 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) = 26.0000 ft/s, acceleration (a) = -27.5000 ft/s², distance (s) = 465.0 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 → Particle Rectilinear Motion