A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 61.0000 ft/s; acceleration (a) = 20.0000 ft/s²; distance (s) = 478.0 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) = 61.0000 ft/s, acceleration (a) = 20.0000 ft/s², distance (s) = 478.0 ft.

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

5. Step 5 — Evaluate:

   $$v = 151.1\ \text{ft/s}$$

6. Step 6 — Check: returning v = 151.1 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

• 302.3 — kept a factor of two that cancels in the correct rearrangement.
• 75.5662 — dropped that same factor in the other direction.
• 166.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Non-constant Acceleration

An elevator speeds up with constant acceleration before reaching cruise speed. Given initial velocity (v_0) = 18.5000 ft/s; constant acceleration (a) = 24.6000 ft/s^2; time (t) = 5.4000 s, determine the final velocity (v) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant acceleration.
• 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.
• Constant acceleration kinematics relates initial velocity, final velocity, acceleration, and time for a particle.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v = v_0 + a t$$

2. Step 2 — Rearrange symbolically for v:

   $$v = v_0 + a t$$

3. Step 3 — List the givens: initial velocity (v_0) = 18.5000 ft/s, constant acceleration (a) = 24.6000 ft/s^2, time (t) = 5.4000 s.

4. Step 4 — Substitute the given values:

   $$v = v_0 + 24.6000 5.4000$$

5. Step 5 — Evaluate:

   $$v = 151.3\ \text{ft/s}$$

6. Step 6 — Check: returning v = 151.3 ft/s to

   $$v = v_0 + a t$$

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

Why the other options are there

• 302.7 — kept a factor of two that cancels in the correct rearrangement.
• 75.6700 — dropped that same factor in the other direction.
• 166.5 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Constant Acceleration

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 25.0000 ft/s; distance (s) = 401.0 ft; final velocity (v) = 100.8 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) = 25.0000 ft/s, distance (s) = 401.0 ft, final velocity (v) = 100.8 ft/s.

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

5. Step 5 — Evaluate:

   $$a = 11.8898\ \text{ft/s²}$$

6. Step 6 — Check: returning a = 11.8898 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

• 23.7797 — kept a factor of two that cancels in the correct rearrangement.
• 5.9449 — dropped that same factor in the other direction.
• 13.0788 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Non-constant Acceleration

A dropped object near Earth's surface undergoes constant acceleration due to gravity. Given constant acceleration (a) = 17.3000 ft/s^2; time (t) = 8.9000 s; final velocity (v) = 95.4000 ft/s, determine the initial velocity (v_0) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant acceleration.
• Everything except v_0 is given, so isolate v_0 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.
• Constant acceleration kinematics relates initial velocity, final velocity, acceleration, and time for a particle.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v = v_0 + a t$$

2. Step 2 — Rearrange symbolically for v_0:

   $$v_{0} = v - a t$$

3. Step 3 — List the givens: constant acceleration (a) = 17.3000 ft/s^2, time (t) = 8.9000 s, final velocity (v) = 95.4000 ft/s.

4. Step 4 — Substitute the given values:

   $$v_{0} = 95.4000 - 17.3000 8.9000$$

5. Step 5 — Evaluate:

   $$v_{0} = -58.5700\ \text{ft/s}$$

6. Step 6 — Check: returning v_0 = -58.5700 ft/s to

   $$v = v_0 + a t$$

   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.
• -29.2850 — dropped that same factor in the other direction.
• -64.4270 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Constant Acceleration

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 61.0000 ft/s; acceleration (a) = 16.0000 ft/s²; final velocity (v) = 74.3000 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) = 61.0000 ft/s, acceleration (a) = 16.0000 ft/s², final velocity (v) = 74.3000 ft/s.

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

5. Step 5 — Evaluate:

   $$s = 56.2341\ \text{ft}$$

6. Step 6 — Check: returning s = 56.2341 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

• 112.5 — kept a factor of two that cancels in the correct rearrangement.
• 28.1170 — dropped that same factor in the other direction.
• 61.8575 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Non-constant Acceleration

A car accelerates from a stoplight under constant acceleration. Given initial velocity (v_0) = 11.5000 ft/s; time (t) = 1.2000 s; final velocity (v) = 277.8 ft/s, determine the constant acceleration (a) in ft/s^2.

Start with the thinking

• The governing relation printed in this handbook section is Constant acceleration.
• 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.
• Constant acceleration kinematics relates initial velocity, final velocity, acceleration, and time for a particle.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v = v_0 + a t$$

2. Step 2 — Rearrange symbolically for a:

   $$a = \dfrac{v - v_0}{t}$$

3. Step 3 — List the givens: initial velocity (v_0) = 11.5000 ft/s, time (t) = 1.2000 s, final velocity (v) = 277.8 ft/s.

4. Step 4 — Substitute the given values:

   $$a = \dfrac{277.8 - v_0}{1.2000}$$

5. Step 5 — Evaluate:

   a = 221.9\ \text{ft/s^2}

6. Step 6 — Check: returning a = 221.9 ft/s^2 to

   $$v = v_0 + a t$$

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

Why the other options are there

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

Reference: FE Handbook — Dynamics: Constant Acceleration

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 77.0000 ft/s; acceleration (a) = -26.5000 ft/s²; distance (s) = 285.0 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) = 77.0000 ft/s, acceleration (a) = -26.5000 ft/s², distance (s) = 285.0 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 → Non-constant Acceleration

An elevator speeds up with constant acceleration before reaching cruise speed. Given initial velocity (v_0) = 37.5000 ft/s; constant acceleration (a) = 13.7000 ft/s^2; final velocity (v) = 80.0000 ft/s, determine the time (t) in s.

Start with the thinking

• The governing relation printed in this handbook section is Constant acceleration.
• Everything except t is given, so isolate t 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.
• Constant acceleration kinematics relates initial velocity, final velocity, acceleration, and time for a particle.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v = v_0 + a t$$

2. Step 2 — Rearrange symbolically for t:

   $$t = \dfrac{v - v_0}{a}$$

3. Step 3 — List the givens: initial velocity (v_0) = 37.5000 ft/s, constant acceleration (a) = 13.7000 ft/s^2, final velocity (v) = 80.0000 ft/s.

4. Step 4 — Substitute the given values:

   $$t = \dfrac{80.0000 - v_0}{13.7000}$$

5. Step 5 — Evaluate:

   $$t = 3.1022\ \text{s}$$

6. Step 6 — Check: returning t = 3.1022 s to

   $$v = v_0 + a t$$

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

Why the other options are there

• 6.2044 — kept a factor of two that cancels in the correct rearrangement.
• 1.5511 — dropped that same factor in the other direction.
• 3.4124 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Constant Acceleration

A dynamics problem uses Constant-acceleration kinematics. Given initial velocity (v0) = 32.0000 ft/s; distance (s) = 312.0 ft; final velocity (v) = 12.3000 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) = 32.0000 ft/s, distance (s) = 312.0 ft, final velocity (v) = 12.3000 ft/s.

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

5. Step 5 — Evaluate:

   $$a = -1.3986\ \text{ft/s²}$$

6. Step 6 — Check: returning a = -1.3986 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

• -2.7971 — kept a factor of two that cancels in the correct rearrangement.
• -0.6993 — dropped that same factor in the other direction.
• -1.5384 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Non-constant Acceleration

A dropped object near Earth's surface undergoes constant acceleration due to gravity. Given initial velocity (v_0) = 12.0000 ft/s; constant acceleration (a) = 6.2000 ft/s^2; time (t) = 1.6000 s, determine the final velocity (v) in ft/s.

Start with the thinking

• The governing relation printed in this handbook section is Constant acceleration.
• 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.
• Constant acceleration kinematics relates initial velocity, final velocity, acceleration, and time for a particle.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v = v_0 + a t$$

2. Step 2 — Rearrange symbolically for v:

   $$v = v_0 + a t$$

3. Step 3 — List the givens: initial velocity (v_0) = 12.0000 ft/s, constant acceleration (a) = 6.2000 ft/s^2, time (t) = 1.6000 s.

4. Step 4 — Substitute the given values:

   $$v = v_0 + 6.2000 1.6000$$

5. Step 5 — Evaluate:

   $$v = 21.9200\ \text{ft/s}$$

6. Step 6 — Check: returning v = 21.9200 ft/s to

   $$v = v_0 + a t$$

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

Why the other options are there

• 43.8400 — kept a factor of two that cancels in the correct rearrangement.
• 10.9600 — dropped that same factor in the other direction.
• 24.1120 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Constant Acceleration