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Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12
Browse organized narrated video solutions. Each problem page includes the question, course, book, chapter, and related study links.
Video solutions
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Problem 12-61: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12Two cars start from rest side by side and travel along a straight road. Car A accelerates at $4 \text{ m/s}^2$ for $10$ s and then maintains a constant speed. Car B accelerates at $5 \text{ m/s}^2$ until reaching a const…
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Problem 12-58: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A two-stage rocket is fired vertically from rest with the acceleration described below. **Phase 1 (0 ≤ t < 15 s):** Acceleration increases linearly from 0 to 15 m/s²: $$a_1(t) = t \quad \text{m/s}^2$$ **Phase 2 (15 ≤ t ≤…
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Problem 12-60: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A package is dropped from an elevator at a height of 100 ft above the ground. The elevator maintains a constant upward speed of 4 ft/s. The package is released with the same upward speed as the elevator. Assume gravitati…
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Problem 12-57: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A boat starts from rest at $s = 0$ and travels in a straight line. The acceleration varies as follows: $a$ decreases linearly from $8$ ft/s² to $6$ ft/s² as $s$ goes from $0$ to $100$ ft, then decreases linearly from $6$…
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Problem 12-57: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12Starting from rest at $s = 0$, a boat travels in a straight line with the acceleration described by the following a–s graph: - **Segment 1:** $a = 6$ ft/s² for $0 \le s \le 100$ ft (constant) - **Segment 2:** $a$ decreas…
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Problem 12-37: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12Starting from rest at $s = 0$, a boat travels in a straight line with the following piecewise acceleration–position profile: - $a = 8$ ft/s² for $0 \leq s \leq 100$ ft - $a = 6$ ft/s² for $100 \text{ ft} \leq s \leq 150$…
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Problem 12-56: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12Starting from rest at $s = 0$, a boat travels in a straight line with the acceleration described by the following piecewise linear a-s graph: - From $s = 0$ to $s = 100$ ft: acceleration decreases linearly from $a = 8$ f…
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Problem 12-54: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12The v–t graph for a car moving along a straight road is given by $v = 0.6t^2$ for $0 \le t \le 5$ s, and a straight line from $v = 15$ m/s at $t = 5$ s to $v = 0$ at $t = 15$ s. At $t = 0$, $s = 0$. 1. Determine the $s$–…
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Problem 12-53: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A motorcycle starts from rest at $s = 0$ and travels along a straight road with the speed shown by a $v$–$t$ graph. The graph consists of three segments: $$v(t) = \begin{cases} 1.25t & 0 \le t \le 4\text{ s} \\ 5 & 4 < t…
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Problem 12-52: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A motorcycle starts from rest at $s = 0$ and travels along a straight road with the speed described by the following piecewise v–t graph: $$v(t) = \begin{cases} 1.25t & 0 \le t \le 4 \ \text{s} \\ 5 & 4 \le t \le 10 \ \t…
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Problem 12-51: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A v–t graph for a train's motion is given with the following segments: - $0 \le t < 60$ s: velocity increases linearly from $0$ to $6$ m/s - $60 \le t \le 120$ s: velocity is constant at $6$ m/s - $120 < t \le 180$ s: ve…
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Problem 12-51: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A v–t graph for a train consists of three segments: - $0 \le t < 60$ s: velocity increases linearly from $0$ to $6$ m/s - $60 \text{ s} \le t \le 120$ s: velocity is constant at $6$ m/s - $120 \text{ s} < t \le 180$ s: v…
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Problem 12-50: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A car starts from rest at $s = 0$ and is subjected to an acceleration defined by the following $a$–$s$ graph: - $a = 12$ ft/s² for $0 \le s \le 300$ ft - $a = -0.04s + 24$ ft/s² for $300 \le s \le 450$ ft (a linear decre…
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Problem 12-49: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A jet car is originally traveling at a velocity of 10 m/s when it is subjected to the following piecewise acceleration: $$a(t) = \begin{cases} 6 \ \text{m/s}^2 & 0 \le t < 15 \ \text{s} \\ -4 \ \text{m/s}^2 & t \ge 15 \ …
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Problem 12-48: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A race car starts from rest and travels along a straight road until it reaches a speed of 26 m/s in 8 s. The $v$–$t$ graph consists of three segments: $$v = \begin{cases} 3.5t & 0 \leq t < 4 \text{ s} \\ 14 & 4 \text{ s}…
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Problem 12-47: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A two-stage rocket is fired vertically from rest at $s = 0$ with the acceleration described by the graph below. $$a(t) = \begin{cases} \dfrac{2}{5}\,t \; \text{m/s}^2 & 0 \le t < 30 \text{ s} \\ 24 \; \text{m/s}^2 & 30 \…
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Problem 12-46: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A rocket moves along a straight track starting from rest ($v = 0$ at $s = 0$). Its acceleration–position relationship is: $$a(s) = \begin{cases} 5 \ \text{ft/s}^2 & 0 \leq s \leq 100 \ \text{ft} \\ 5 + 6\left(\sqrt{s} - …
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Problem 12-43: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A jet plane lands on a runway with an initial speed of $v_0 = 300 \text{ ft/s} = 91.44 \text{ m/s}$ at $t = 0$ s (with $s_0 = 0$). The acceleration–time graph is piecewise: $$a(t) = \begin{cases} 0 & 0 \le t \le 10 \text…
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Problem 12-44: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A particle travels between two plates spaced 200 mm apart. Its $v$–$t$ graph has a symmetric triangular shape: the particle accelerates from rest at a constant $a = +4 \text{ m/s}^2$ to a peak velocity $v_{\max}$, then d…
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Problem 12-42: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12The velocity of a car is plotted as a $v$–$t$ graph. From $t = 0$ to $t = 40$ s the velocity is constant at $v = 10$ m/s. From $t = 40$ s to $t = 80$ s the velocity decreases linearly from $10$ m/s to $0$ m/s. Determine …
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Problem 12-43: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12The motion of a jet plane just after landing on a runway is described by a piecewise constant acceleration–time graph with two segments: $a = -20$ ft/s² for $0 \le t \le 5$ s, and $a = -3$ ft/s² for $5\text{ s} \le t \le…
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Problem 12-48: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A race car starts from rest and travels along a straight road until it reaches a speed of 26 m/s in 8 s. The v–t graph consists of three segments: - **Segment 1** ($0 \le t \le 6$ s): parabolic, $v = \dfrac{t^2}{1.8}$ m/…
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Problem 12-50: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A car starts from rest at $s = 0$ and is subjected to an acceleration shown by the $a$–$s$ graph, where $a = 6$ ft/s² (constant) for $0 \leq s \leq 200$ ft. Draw the $v$–$s$ graph and determine the time needed to travel …
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Problem 12-47: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A two-stage rocket is fired vertically from rest at $s = 0$. During Stage A ($0 \leq t \leq 30$ s) the rocket has a constant acceleration of $15 \text{ m/s}^2$. At $t = 30$ s, Stage A burns out and Stage B ignites with a…
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Problem 12-46: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12The $a$–$s$ graph for a rocket moving along a straight track has been experimentally determined. The graph consists of two segments: - **Linear segment:** $a = 6 + 0.08s$ (ft/s²) for $0 \le s \le 75$ ft - **Nonlinear seg…
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Problem 12-45: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A particle moves through an electric field between two plates. Its velocity varies as a half-sine wave with $t' = 0.2$ s and $v_{\max} = 10$ m/s: $$v(t) = 10\sin(5\pi t) \quad [\text{m/s}], \quad 0 \le t \le 0.2 \ \text{…
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Problem 12-44: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12A particle moves through an electric field from one plate to another. Its v–t graph is triangular (tent-shaped): the particle accelerates from rest at a constant $a = +4 \text{ m/s}^2$, reaches a peak velocity $v_{\max}$…
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Problem 12-39: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12The velocity of a car is plotted on a v–t graph as follows: the car travels at a constant velocity of 6 m/s from $t = 0$ s to $t = 40$ s, then its velocity decreases linearly from 6 m/s at $t = 40$ s to 0 m/s at $t = 80$…
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Problem 12-41: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12An elevator starts from rest at ground level. It can accelerate at $5 \text{ ft/s}^2$ and then decelerate at $2 \text{ ft/s}^2$. Determine the shortest time it takes to reach a point $40 \text{ ft}$ above the starting po…
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Problem 12 1 Dynamics Hibbeler
Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12Starting from rest, a particle moving in a straight line has an acceleration of a = (2t - 6) m/s^2, where t is in seconds. What is the particle’s velocity when t = 6 s, and what is its position when t = 11 s? Please co…