Dynamics is 4 to 6 questions on the FE Civil exam, the smallest of the mechanics areas, and it is the one civil candidates most often write off. That is a mistake at four to six points: the problem types repeat, and most of them come down to picking between kinematic equations, work-energy, and impulse-momentum before you write anything.
The solutions below state which method was chosen and why, since that decision is where most of the time is lost. They also keep units explicit, because dynamics is where slugs, pounds-mass and the 32.2 factor quietly ruin an otherwise correct setup. Each problem is sized to the two-minute pace you need on exam day.
Exam weight: NCEES lists Dynamics at 4-6 questions (4-6%) of the 110-question FE Civil exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Dynamics
NCEES allots 4 to 6 dynamics questions on the 110-question FE Civil exam, about 4 to 6 percent. Coverage starts with particle kinematics: constant acceleration along a line, projectile motion split into independent horizontal and vertical components, and curvilinear motion in normal and tangential coordinates where the normal acceleration is v squared over the radius of curvature.
Kinetics follows: Newton's second law applied to a block on an incline or a vehicle braking, work and energy including springs and gravity, and impulse-momentum with direct-impact collisions and the coefficient of restitution. Rigid-body rotation about a fixed axis appears too, which means mass moment of inertia and the parallel axis theorem in its rotational form.
5 Free Dynamics Practice Problems
Each problem below comes from the PECivilClick FE Civil question bank and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1
A particle moves along a line with position \( s(t) = 5t^2 - 2t \) (m), \( t \) in seconds. What is the velocity at \( t = 3\,\mathrm{s} \)?
A) \( 18\,\mathrm{m/s} \)
B) \( 22\,\mathrm{m/s} \)
C) \( 28\,\mathrm{m/s} \)
D) \( 32\,\mathrm{m/s} \)
Answer: C) \( 28\,\mathrm{m/s} \)
Step 1 – Identify given information:
| Position function | \( s(t) = 5t^2 - 2t \) (m) |
| Time of interest | \( t = 3\,\text{s} \) |
| Find | Velocity \( v(3) \) |
Step 2 – Velocity is the first derivative of position: From the FE Handbook, \( v(t) = \frac{ds}{dt} \).
Step 3 – Differentiate and substitute:
\( v = \frac{ds}{dt} = \frac{d}{dt}(5t^2 - 2t) = 10t - 2 \)
At \( t = 3\,\text{s} \):
\( v(3) = 10(3) - 2 = 30 - 2 = 28\,\text{m/s} \)
Step 4 – Answer: The velocity at \( t = 3\,\text{s} \) is \( 28\,\text{m/s} \). Option (A) 18 m/s would result from using \( v = 6t \) (wrong derivative); option (B) 22 uses an incorrect coefficient. The correct answer is (C).
Problem 2
A car’s speed is \( v(t) = 12-0.6t \) (m/s). How far does it travel before stopping?
A) 60 m
B) 96 m
C) 120 m
D) 144 m
Answer: C) 120 m
Step 1 – Identify given information:
| Velocity function | \( v(t) = 12 - 0.6t \) (m/s) |
| Initial speed | \( v(0) = 12\,\text{m/s} \) |
| Find | Distance traveled before stopping |
Step 2 – Distance by integration of velocity: From the FE Handbook, \( s = \int_0^{t_\text{stop}} v(t)\,dt \). First find when \( v = 0 \).
Step 3 – Solve:
Stopping time: \( 12 - 0.6t = 0 \Rightarrow t = \frac{12}{0.6} = 20\,\text{s} \)
\( s = \int_0^{20}(12 - 0.6t)\,dt = \left[12t - 0.3t^2\right]_0^{20} = 12(20) - 0.3(400) = 240 - 120 = 120\,\text{m} \)
Step 4 – Answer: The car travels \( 120\,\text{m} \) before stopping. Options (A) 60 m and (B) 96 m result from integration errors or wrong stopping times. The correct answer is (C).
Problem 3
A projectile is launched at \( v_0 = 40\,\mathrm{m/s} \) on level ground (no air). What launch angle gives a maximum height of \( 30\,\mathrm{m} \)?
A) 22°
B) 30°
C) 37°
D) 53°
Answer: C) 37°
Step 1 – Identify given information:
| Launch speed | \( v_0 = 40\,\text{m/s} \) |
| Maximum height | \( H = 30\,\text{m} \) |
| Find | Launch angle \( \theta \) |
Step 2 – Maximum height formula solved for angle: \( H = \frac{v_0^2 \sin^2\theta}{2g} \Rightarrow \sin^2\theta = \frac{2gH}{v_0^2} \).
Step 3 – Substitute and solve:
\( \sin^2\theta = \frac{2(9.81)(30)}{(40)^2} = \frac{588.6}{1600} = 0.3679 \)
\( \sin\theta = 0.6066 \Rightarrow \theta = \arcsin(0.6066) \approx 37^\circ \)
Step 4 – Answer: The launch angle is approximately \( 37^\circ \). This is a classic complementary-angle problem; \( 53^\circ \) would give the same range but a different height. The correct answer is (C).
Problem 4
Position is \( \vec{r}(t) = 3t\,\mathbf{i} + 4t^2\,\mathbf{j} \) (m). Find speed at \( t = 2\,\mathrm{s} \).
A) 12.0 m/s
B) 14.4 m/s
C) 16.3 m/s
D) 18.0 m/s
Answer: C) 16.3 m/s
Step 1 – Identify given information:
| Position vector | \( \vec{r}(t) = 3t\,\mathbf{i} + 4t^2\,\mathbf{j} \) (m) |
| Time | \( t = 2\,\text{s} \) |
| Find | Speed \( |\vec{v}| \) at \( t = 2\,\text{s} \) |
Step 2 – Velocity from differentiation: \( \vec{v} = \frac{d\vec{r}}{dt} \), and speed is the magnitude \( |\vec{v}| = \sqrt{v_x^2 + v_y^2} \).
Step 3 – Differentiate and evaluate:
\( \vec{v} = \frac{d\vec{r}}{dt} = 3\,\mathbf{i} + 8t\,\mathbf{j} \)
At \( t = 2\,\text{s} \): \( \vec{v}(2) = 3\,\mathbf{i} + 16\,\mathbf{j} \)
\( |\vec{v}| = \sqrt{3^2 + 16^2} = \sqrt{9 + 256} = \sqrt{265} \approx 16.3\,\text{m/s} \)
Step 4 – Answer: The speed at \( t = 2\,\text{s} \) is \( 16.3\,\text{m/s} \). A common error is confusing position magnitude with velocity magnitude. The correct answer is (C).
Problem 5
A cart starts at \( v_0 = 20\,\mathrm{m/s} \) and accelerates at \( a = 1.5\,\mathrm{m/s}^2 \) for \( 8\,\mathrm{s} \). How far does it travel?
A) 160 m
B) 192 m
C) 208 m
D) 224 m
Answer: C) 208 m
Step 1 – Identify given information:
| Initial velocity | \( v_0 = 20\,\text{m/s} \) |
| Acceleration | \( a = 1.5\,\text{m/s}^2 \) |
| Time | \( t = 8\,\text{s} \) |
| Find | Displacement \( s \) |
Step 2 – Constant-acceleration displacement formula: From the FE Handbook, \( s = v_0 t + \frac{1}{2}at^2 \).
Step 3 – Substitute and solve:
\( s = 20(8) + \frac{1}{2}(1.5)(8)^2 = 160 + \frac{1}{2}(1.5)(64) = 160 + 48 = 208\,\text{m} \)
Step 4 – Answer: The cart travels \( 208\,\text{m} \). Option (A) 160 m neglects the acceleration term; option (D) 224 m uses \( a = 2\,\text{m/s}^2 \). The correct answer is (C).
Using the FE Reference Handbook for Dynamics
The handbook's dynamics section gives the constant-acceleration equations, the normal and tangential acceleration components, and a mass moment of inertia table for common bodies. Search for the body shape rather than scrolling. One thing it will not do is choose your method, so decide between energy and momentum first, then go find the equation.
Four Mistakes That Cost Points
- Reaching for kinematics when energy is faster If a problem gives you positions and speeds but never asks about time, work-energy will beat the kinematic equations by a wide margin. Scan the question for the word time before you commit; its absence is the tell that energy or momentum is the intended route.
- Mixing mass and weight in USCS units A 100 pound block does not have a mass of 100. Divide the weight by 32.2 to get slugs before it goes into F equals ma or one half m v squared. Write the unit beside every number as you substitute and the error surfaces immediately.
- Treating projectile range as a memorized formula The range equation only holds when launch and landing are at the same elevation. On the exam the ball often leaves a cliff or lands on a roof, so split the motion into vertical and horizontal, solve the vertical for flight time, then multiply.
- Assuming momentum problems conserve energy Momentum is conserved in every impact; kinetic energy is conserved only when the collision is perfectly elastic. If the problem gives a coefficient of restitution below one, or says the bodies move off together, energy is lost and the energy equation will give you a wrong answer.
Frequently Asked Questions
How many dynamics questions are on the FE Civil exam?
NCEES lists 4 to 6 dynamics questions out of 110, roughly 4 to 6 percent. It is a small area, but it is also a narrow one: kinematics, Newton's second law, work-energy, impulse-momentum and rigid-body rotation cover essentially all of it, so a focused weekend can move you from guessing to reliable.
Is FE Civil dynamics worth studying if it is only a few questions?
Yes, because the cost is low. Four to six questions out of 110 is a meaningful slice of the margin between pass and fail, and the topic list is short enough to cover in a few focused sessions. Skipping it concedes points that are cheaper to earn than almost anywhere else on the exam.
Does FE Civil dynamics include rigid-body motion or only particles?
Both, but rigid bodies stay simple. Expect rotation about a fixed axis, mass moment of inertia from the handbook table, and the rotational form of the parallel axis theorem. General plane motion with instantaneous centers and rolling constraints shows up far less often than in a university dynamics course.
What is the fastest way to practice dynamics for the FE?
Work problems in mixed order rather than by topic. When every question in a set is a projectile, you never practice the actual exam skill, which is deciding in the first fifteen seconds whether the problem is kinematics, kinetics, energy or momentum. Mixed sets force that decision every time.
Keep Going
Work through the other FE Civil knowledge areas with more free practice problems, review the full FE Civil exam topic breakdown, or plan your preparation with our FE exam study guide and study timeline.