test 1

1. 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

2. The average speed is defined as __________.
A) Dr/Dt B) Ds/Dt
C) sT/Dt D) None of the above.

1. 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 

2. 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

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 

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

The slope of a v-t graph at any instant represents instantaneous

A) velocity. B) acceleration.
C) position. D) jerk.

. 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

. 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

The particle in Problem 1 stops moving at t = _______.
A) 10 s B) 20 s
C) 30 s D) 40 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

Select the correct a-t graph for the velocity curve shown.
A) linear up curved down B)flat zero flat up
C) linear up linear down D) flat zero negative flat

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.

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.

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

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

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  i m/s
D) 1.25  j m/s rad=5m

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

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.

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

In a projectile motion problem, what is the maximum number of unknowns that can be solved?

A) 1 B) 2

C) 3 D) 4

The time of flight of a projectile, fired over level ground, with initial velocity Vo at angle θ, is equal to?

A) (vo sin q) B) (2vo sin q)

C) (vo cos q) D) (2vo cos q)

A projectile is given an initial velocity
vo at an angle f 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.

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

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.

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.

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

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/s2 B) 8.6 m/s2
C) 3.2 m/s2 D) 11.2 m/s2

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 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.

In a polar coordinate system, the velocity vector can be written as v = vrur + vθuθ = rur + rquq. The term theta dot is called
A) transverse velocity. B) radial velocity.
C) angular velocity. D) angular acceleration

The speed of a particle in a cylindrical coordinate system is

A) r dot B) r theta dot

C) sqrt (rtheta dot)2 + (rdot)2 D) sqrt (rtheta dot)2 + (rdot)2 + (zdot)2

If r 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.

If a particle moves in a circular path with constant velocity, its radial acceleration is

A) zero. B) r dot dot

C) − rthetadot ^2. D) 2rdotthetadot .

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.

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

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.

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.

Determine the speed of block B.

A) 1 m/s B) 2 m/s

C) 4 m/s D) None of the above.
two pulleys 2m/s 3 strings block at bottom 2vb va

. 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.

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 B) 3 ft/s
C) 12 ft/s D) 9 ft/s

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

The velocity of B relative to A is defined as

A) vB – vA . B) vA – vB .
C) vB + vA . D) vA + vB .

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

Two particles, A and B, are moving in the directions shown. What should be the angle theta so that vB/A is minimum? B up and to the right 4ft/s A to right 3ft/s

A) 0° B) 180°
C) 90° D) 270°

. 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
b to left 700km/h a down and right 30deg 600km/h

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
b flat right 100 a up left 6o @ 30deg

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
b up to right theta 4ft/s a righ 3ft/s

Newton’s second law can be written in mathematical form as F = ma. Within the summation of forces, F, ________ are(is) not included.
A) external forces B) weight
C) internal forces D) All of the above.

The equation of motion for a system of n-particles can be written as Fi =  miai = maG, where aG indicates _______.
A) summation of each particle’s acceleration
B) acceleration of the center of mass of the system
C) acceleration of the largest particle
D) None of the above.

The block (mass = m) is moving upward with a speed v. Draw the FBD if the kinetic friction coefficient is k.

A) mg down N ukN up right B) mg down ukN down left


C) mg down ukmg up right D) None of the above.

Packaging for oranges is tested using a machine that exerts ay = 20 m/s2 and ax = 3 m/s2, simultaneously. Select the correct FBD and kinetic diagram for this condition.

A) W down Rx righht Ry up max right may up B) w down rx right ry up max right
C) ry up may up D) w down ry up may up max up

Internal forces are not included in an equation of motion analysis because the internal forces are_____
A) equal to zero.
B) equal and opposite and do not affect the calculations.
C) negligibly small.
D) not important.

. A 10 lb block is initially moving down a ramp with a velocity of v. The force F is applied to bring the block to rest. Select the correct FBD. f up to right

A) uk10 right B) uk10 left C) ukn right

In dynamics, the friction force acting on a moving object is always ________
A) in the direction of its motion. B) a kinetic friction.
C) a static friction. D) zero.

. If a particle is connected to a spring, the elastic spring force is expressed by F = ks . The “s” in this equation is the
A) spring constant.
B) un-deformed length of the spring.
C) difference between deformed length and un-deformed length.
D) deformed length of the spring.

If the cable has a tension of 3 N, determine the acceleration of block B.
A) 4.26 m/s2  B) - 4.26 m/s2 
C) 8.31 m/s2  D) -8.31 m/s2 
10kg uk=.4 4kg weight

. Determine the acceleration of the block.
A) 2.20 m/s2  B) 3.17 m/s2 
C) 11.0 m/s2  D) 4.26 m/s2 
triang pulled 30deg 60N force down 5kg weight

Determine the tension in the cable when the 400 kg box is moving upward with a 4 m/s2 acceleration.
A) 2265 N B) 3365 N
C) 5524 N D) 6543 N
block triangle pulley t up a=4m/s2

A 10 lb particle has forces of F1= (3i + 5j) lb and
F2= (-7i + 9j) lb acting on it. Determine the acceleration of the particle.
A) (-0.4 i + 1.4 j) ft/s2 B) (-4 i + 14 j) ft/s2
C) (-12.9 i + 45 j) ft/s2 D) (13 i + 4 j) ft/s2

The “normal” component of the equation of motion is written as Fn=man, where Fn is referred to as the _______.

A) impulse B) centripetal force
C) tangential force D) inertia force

The positive n direction of the normal and tangential coordinates is ____________.

A) normal to the tangential component
B) always directed toward the center of curvature
C) normal to the bi-normal component
D) All of the above.

A 10 kg sack slides down a smooth surface. If the normal force at the flat spot on the surface, A, is 98.1 N () , the radius of curvature is ____ v=2m/s

A) 0.2 m B) 0.4 m

C) 1.0 m D) None of the above

A 20 lb block is moving along a smooth surface. If the normal force on the surface at A is 10 lb, the velocity is ________.

A) 7.6 ft/s B) 9.6 ft/s

C) 10.6 ft/s D) 12.6 ft/s
p=7ft

The tangential acceleration of an object
A) represents the rate of change of the velocity vector’s direction.
B) represents the rate of change in the magnitude of the velocity.
C) is a function of the radius of curvature.
D) Both B and C.

The block has a mass of 20 kg and a speed of
v = 30 m/s at the instant it is at its lowest point. Determine the tension in the cord at this instant.
A) 1596 N B) 1796 N
C) 1996 N D) 2196 N

The normal force which the path exerts on a particle is always perpendicular to the _________
A) radial line. B) transverse direction.
C) tangent to the path. D) None of the above.

When the forces acting on a particle are resolved into cylindrical components, friction forces always act in the __________ direction.
A) radial B) tangential
C) transverse D) None of the above.

When a pilot flies an airplane in a
vertical loop of constant radius r at
constant speed v, his apparent weight
is maximum at
A) Point A B) Point B (top of the loop)
C) Point C D) Point D (bottom of the loop)

If needing to solve a problem involving the pilot’s weight at Point C, select the approach that would be best.
A) Equations of Motion: Cylindrical Coordinates
B) Equations of Motion: Normal & Tangential Coordinates
C) Equations of Motion: Polar Coordinates
D) No real difference – all are bad.
E) Toss up between B and C.

For the path defined by r = theta^ 2 , the angle y at theta = 0.5 rad is
A) 10º B) 14º
C) 26º D) 75º

If r = theta^2 and theta = 2t, find the magnitude of rdot and theta dot dot when
t = 2 seconds.
A) 4 cm/sec, 2 rad/sec2 B) 4 cm/sec, 0 rad/sec2
C) 8 cm/sec, 16 rad/sec2 D) 16 cm/sec, 0 rad/sec2