Dynamics Chapter 12

0.0 ft s = s0 + v0t + ½ at^2 ; s = (0) + (-3)(3) + .5(2)(3)^2 = -9 + 9 = 0

A particle has an initial velocity of 3 ft/s to the left at s0 = 0 ft. Determine its position when t = 3 s if the acceleration is 2 ft/s2 to the right. A) 0.0 ft B) 6.0 ft ← C) 18.0 ft → D) 9.0 ft →

0 ft/s (Can we calculate average speed from this problem statement? No! We do not know the total path distance)

A particle has an initial velocity of 30 ft/s to the left. If it then passes through the same location 5 seconds later with a velocity of 50 ft/s to the right, the average velocity of the particle during the 5 s time interval is _______. A) 10 ft/s → B) 40 ft/s → C) 16 m/s → D) 0 ft/s

φ = 90° (v^2)y = (v^2)y - 2g(y-yo) @ max y vy = 0 and 2g(y-yo) = (vosin θ)2 which is max. @ θ = 90

A particle has an initial velocity vo at angle φ with respect to the horizontal. The maximum height it can reach is when A) φ = 30° B) φ = 45° C) φ = 60° D) φ = 90°

100 ft v^2 = v02 + 2ac(s - so); (30)^2 = (12)^2 + 2(3.78)(s - 0); s = 100 ft

A particle is moving with an initial velocity of v = 12 ft/s and constant acceleration of 3.78 ft/s2 in the same direction as the velocity. Determine the distance the particle has traveled when the velocity reaches 30 ft/s A) 50 ft B) 100 ft C) 150 ft D) 200 ft

1.6 m/s2 ←

A particle moves along a horizontal path with its velocity varying with time as shown. The average acceleration of the particle is _________. A) 0.4 m/s2 → B) 0.4 m/s2 ← C) 1.6 m/s2 → D) 1.6 m/s2 ←

5 m/s2 a = [42+(302/300)2]1/2=5

A particle traveling in a circular path of radius 300 m has an instantaneous velocity of 30 m/s and its velocity is increasing at a constant rate of 4 m/s2. What is the magnitude of its total acceleration at this instant? A) 3 m/s2 B) 4 m/s2 C) 5 m/s2 D) -5 m/s2

less than

A projectile is given an initial velocity vo at an angle φ above the horizontal. The velocity of the projectile when it hits the slope is ____________ the initial velocity vo. A) less than B) equal to C) greater than D) None of the above.

angular velocity

A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration.

(48i - 30j ) km/h vA=52i+30j, vB=100i

Determine the relative velocity of particle B with respect to particle A. A) (48i + 30j) km/h B) (- 48i + 30j ) km/h C) (48i - 30j ) km/h D) (- 48i - 30j ) km/h

12 ft/s up vA + 2vB + vC = 0, Thus, 6 + 2vB +18 = 0, Hence, vB = -12 (up)

Determine the speed of block B when block A is moving down at 6 ft/s while block C is moving down at 18 ft/s . A) 24 ft/s dn B) 3 ft/s up C) 12 ft/s up D) 9 ft/s dn

1 m/s up SA +2 SB = L, Thus, VB = -0.5 VA

Determine the speed of block B. A) 1 m/s up B) 2 m/s dn C) 4 m/s up D) None of the above.

(1220 i - 300 j ) km/hr vA/B=vA-vB = [519.6-(-700)]i + (-300-0)j = 1220i-300j

Determine the velocity of plane A with respect to plane B. A) (400 i + 520 j ) km/hr B) (1220 i - 300 j ) km/hr C) (-181 i - 300 j ) km/hr D) (-1220 i + 300 j ) km/hr

(4i + 3j) m/s 2sA + sB = l, 2vA + vB =0, Thus, vA = -0.5vB (i.e. vA = 5[(4/5) i + (3/5) j]

Determine the velocity vector of block A when block B is moving downward with a speed of 10 m/s. A) (8i + 6j) m/s B) (4i + 3j) m/s C) (-8i - 6j) m/s D) (3i + 4j) m/s

v-t

Displacement of a particle over a given time interval equals the area under the ___ graph during that time. A) a-t B) a-s C) v-t C) s-t

velocity vector

For a particle with curvilinear motion, which of the following is always tangential to the motion path? Acceleration vector Position vector Velocity vector None of the above

4 s The tangent to the curve is the acceleration = 12.5m/s2 constant (constant dv/dt slope). s = so+vot+.5at^2. Thus, solving for t, t = 4 s.

If a car has the velocity curve shown, determine the time t necessary for the car to travel 100 meters. A) 8 s B) 4 s C) 10 s D) 6 s

2.5 i m/s (r = 0i+0j, r'=10i+0j; Δr/Δt=vavg=(10/4)i=2.5i)

If a particle has moved from A to B along the circular path in 4s, what is the average velocity of the particle? A) 2.5 i m/s B) 2.5 i +1.25 j m/s C) 1.25 π i m/s D) 1.25 π j m/s

zero

If a particle moves along a curve with a constant speed, then its tangential component of acceleration is A) positive. B) negative. C) zero. D) constant.

8.6 m/s a=[((8)(1))2+(((4)(1)2 )2/5)2]=8.6

If a particle moving in a circular path of radius 5 m has a velocity function v = 4t2 m/s, what is the magnitude of its total acceleration at t = 1 s? A) 8 m/s B) 8.6 m/s

100 m/s

If a particle starts from rest and accelerates according to the graph shown, the particle's velocity at t = 20 s is A) 200 m/s B) 100 m/s C) 0 D) 20 m/s

moving in a circular path

If r dot is zero for a particle, the particle is A) not moving. B) moving in a circular path. C) moving on a straight line. D) moving with constant velocity.

should be directed along the path of motion.

If the motion of one particle is dependent on that of another particle, each coordinate axis system for the particles _______ A) should be directed along the path of motion. B) can be directed anywhere. C) should have the same origin. D) None of the above.

5 m/s

If the position of a particle is defined by r = [(1.5t2 + 1) i + (4t - 1) j ] (m), its speed at t = 1 s is A) 2 m/s B) 3 m/s C) 5 m/s D) 7 m/s

25 ft vA=3i, vB=4j, vB/A=-3i+4j, rB/A = 5 fps*5s=25 ft

If theta equals 90° and A and B start moving from the same point, what is the magnitude of rB/A at t = 5 s? A) 20 ft B) 15 ft C) 18 ft D) 25 ft

3 Three independent equations & three unknowns: x = xo + (vox) t , vy = voy - g t, and y = yo + (voy) t - ½ g t

In a projectile motion problem, what is the maximum number of unknowns that can be solved? A) 1 B) 2 C) 3 D) 4

tangent to the hodograph.

In curvilinear motion, the direction of the instantaneous acceleration is always A) tangent to the hodograph. B) perpendicular to the hodograph. C) tangent to the path. D) perpendicular to the path

tangent to the path.

In curvilinear motion, the direction of the instantaneous velocity is always A) tangent to the hodograph. B) perpendicular to the hodograph. C) tangent to the path. D) perpendicular to the path.

only a mass

In dynamics, a particle is assumed to have _________. A) both translation and rotational motions B) only a mass C) a mass but the size and shape cannot be neglected D) no mass or size or shape, it is just a point

D

Select the correct a-t graph for the velocity curve shown.

two

Since two-dimensional vector addition forms a triangle, there can be at most _________ unknowns (either magnitudes and/or directions of the vectors). A) one B) two C) three D) four

sT/Δt

The average speed is defined as __________. A) Δr/Δt B) Δs/Δt C) sT/Δt D) None of the above.

collinear.

The directions of the tangential acceleration and velocity are always A) perpendicular to each other. B) collinear. C) in the same direction. D) in opposite directions.

9.81 m/s2.

The downward acceleration of an object in free-flight motion is A) zero. B) increasing with time. C) 9.81 m/s2. D) 9.81 ft/s2

constant

The horizontal component of velocity remains _________ during a free-flight motion. A) zero B) constant C) at 9.81 m/s2 D) at 32.2 ft/s2

inversely proportional to radius of curvature

The magnitude of the normal acceleration is A) proportional to radius of curvature. B) inversely proportional to radius of curvature. C) sometimes negative. D) zero when velocity is constant.

the time rate of change in the direction of the velocity

The normal component of acceleration represents A) the time rate of change in the magnitude of the velocity. B) the time rate of change in the direction of the velocity. C) magnitude of the velocity. D) direction of the total acceleration.

2 m/s vy = dy/dt = d(0.5x^2)/dt = x(dx/dt) = xvx = (2)(1) = 2

The path of a particle is defined by y = 0.5x2. If the component of its velocity along the x-axis at x = 2 m is vx = 1 m/s, its velocity component along the y-axis at this position is ____. A) 0.25 m/s B) 0.5 m/s C) 1 m/s D) 2 m/s

(8 i -16 j ) m/s2 x = 4t2, y = 2x = 8t2, r = 4t2i - 8t2j, dr/dt = v = 8ti - 16tj; dv/dt = a = 8i-16j

The position of a particle is given as r = (4t2 i - 2x j) m. Determine the particle's acceleration. A) (4 i +8 j ) m/s2 B) (8 i -16 j ) m/s2 C) (8 i ) m/s2 D) (8 j ) m/s2

All of the above

The radial component of acceleration of a particle moving in a circular path is always A) negative. B) directed toward the center of the path. C) perpendicular to the transverse component of acceleration. D) All of the above.

zero

The radial component of velocity of a particle moving in a circular path is always A) zero. B) constant. C) greater than its transverse component. D) less than its transverse component

acceleration.

The slope of a v-t graph at any instant represents instantaneous A) velocity. B) acceleration. C) position. D) jerk.

(2vo sin θ)/g Set y = y0 in y equation and solve for t : y = y0 + v0sinθt - 0.5gt2 → t = (2 v0sinθ)/g

The time of flight of a projectile, fired over level ground, with initial velocity Vo at angle θ, is equal to? A) (vo sin θ)/g B) (2vo sin θ)/g C) (vo cos θ)/g D) (2vo cos θ)/g

vB - vA .

The velocity of B relative to A is defined as A) vB - vA . B) vA - vB . C) vB + vA . D) vA + vB .

vA= - vB Note: by definition your coordinate system datum must be aligned with the direction of motion so the ramp angles have no effect.

Two blocks are interconnected by a cable. Which of the following is correct? A) (vx)A= - (vx)B B) vA= - vB C) (vy)A= - (vy)B D) All of the above.

0

Two particles, A and B, are moving in the directions shown. What should be the angle θ so that vB/A is minimum? A) 0° B) 180° C) 90° D) 270°

always dependent

When particles are interconnected by a cable, the motions of the particles are ______ A) always independent. B) always dependent. C) not always dependent. D) None of the above