DYNAMICS

Q.51 If a body moves in such a way that its velocity increases by equal amount in equal intervals

of time, it is said to be moving with

a) a uniform retardation

b) a uniform acceleration

c) a variable acceleration

d) a variable retardation

Q.52 Equation of motion of a point in a straight line, is

a) v = u+ft

b) s = ut + 1/2ft2

c) 2fs = v2 – u2

d) all the above

Q.53 Time required to stop a car moving with a velocity 20m/s within a distance of 40m, is

a) 2 sec

b) 3 sec

c) 4 sec

d) none of these

Q.54 The velocity of a body fallen from height h, on reaching the ground is given by

a) v = 2gh

b) v = 2gh2

c) v = sqrt(2gh)

d) h2/2gh

Q.55 A particle moves with a velocity of 2m/s in a straight line with a negative acceleration of

0.1m/s2. Time taken to traverse a distance of 1.5m is

a) 40 sec

b) 30 sec

c) 20 sec

d) 15 sec

Q.56 A ball is thrown vertically upward with a speed of 15 m/s. Determine the time of flight

when it returns to its original position.

a) 3.0 sec

b) 3.06 sec

c) 3.1 sec

d) 3.3 sec

Q.57 A particle travels along a straight line with a velocity of v = (4t – 3t2) m/sec, where t is in

seconds. Determine the position of the particle when t = 4 sec. s = 0 when t= 0.

a) 30 m

b) 35 m

c) 36 m

d) 32 m

Q.58 A particle travels along a straight line with a speed v = (0.5t3 – 8t) m/s, where t is in

seconds. Determine the acceleration of the particle when t = 2 s.

a) 2m/s2

b) 3 m/s2

c) 4 m/s2

d) None of these

Q.59 The position of the particle is given by s = (2t2 - 8t + 6) m, where t is in seconds.

Determine the time when the velocity of the particle is zero, and the total distance traveled by the

particle when t = 3 s.

a) 12m

b) 8m

c) 10m

d)11m

Q60 A train starts from rest at a station and travels with a constant acceleration of 1 m/s2.

Determine the velocity of the train when t= 30 s and the distance traveled during this time.

a) 30m/s & 450m

b) 32m/s & 430m

c) 34m/s & 400m

d) None of these

Q.61 A car has an initial speed of 25 m/s and a constant deceleration of 3 m/s2. Determine the

velocity of the car when t = 4 s. What is the displacement of the car during the 4-s time interval?

How much time is needed to stop the car?

a)13m/s, 76m & 8.33s

b) 14m/s, 74m & 8.47s

c) 11m/s, 72m & 8.20s

d)10m/s, 71m & 8.0s

Q.62 A particle travels along a straight line with a velocity v = (12 – 3t2) m/s, where t is in

seconds. When t= 1 s, the particle is located 10 m to the left of the origin. Determine the

acceleration when t = 4 s, the displacement from t = 0 to t = 10 s, and the distance the particle

travels during this time period.

a) – 24 m/s2 & 912m

b) - 22 m/s2 & 900m

c) -21 m/s2 & 812m

d) None of these

Q.63 A ball is thrown with an upward velocity of 5 m/s from the top of a 10m high building. One

second later another ball is thrown vertically from the ground with a velocity of 10 m/s.

Determine the height from the ground where the two balls pass each other.

a) 4.0m

b) 4.8m

c) 4.54m

d) 4.75m

Q.65 A car starts from rest and moves with a constant acceleration of 1 .5 m/s2 until it achieves a

velocity of 25 m/s. It then travels with constant velocity for 60 seconds. Determine the average

speed and the total distance traveled.

a) 1708m & 22.3m/s

b) 1728m & 22.8m/s

c) 1710m & 22.7m/s

d) 1704m & 22.0m/s

Q.66 The acceleration of a particle traveling along a straight line is a = (0.02et) m/s2, where t is

in seconds. If v = 0, s = 0 when t = 0, determine the velocity and acceleration of the particle at s

= 4 m.

a) 4.11 m/s & 4.13 m/s2

b) 4.05m/s & 4.10 m/s2

c) 4.0 m/s & 4.0 m/s2

d) None of these

Q.67 A car travels along a horizontal circular curved road that has a radius of 600 m. If the speed

is uniformly increased at a rate of 2000 km/h2, determine the magnitude of the acceleration at the

instant the speed of the car is 60 km/h.

a) 0.415 m/s2

b) 0.488 m/s2

c) 0.455 m/s2

d) None of these

Q.68 The car passes point A with a speed of 25 m/s after which its speed is defined by v = (25 -

0.15s) m/s. Determine the magnitude of the car's acceleration when it reaches point B, where s =

5 1 .5 m.

a) 2.25 m/s2

b) 2.35 m/s2

c) 2.55 m/s2

d) 2.75 m/s2

Q.69 The jet plane is traveling with a constant speed of 110 m/s along the curved path.

Determine the magnitude of the acceleration of the plane at the instant it reaches point A (y = 0).

a) 26.9 m/s2

b) 25.9 m/s2

c) 24 m/s2

d) 23.3 m/s2

Q.70 The ball is kicked with an initial speed VA = 8 m/s at an angle øA = 40° with the horizontal.

Find the equation of the path, y = f(x), and then determine the normal and tangential components

of its acceleration when t = 0.25 s.

a) 3.94 m/s2 & 8.98 m/s

2

b) 3.90 m/s2 & 8.80 m/s2

c) 3.98 m/s2 & 8.50 m/s2

d) 3.40 m/s2 & 8.58 m/s2

Q.71 If motor M exerts a force of F = (10t2 + 100) N on the cable, where t is in seconds,

determine the velocity of the 25-kg crate when t = 4 s . The coefficients of static and kinetic

friction between the crate and the plane are µs = 0.3 and µk = 0.25, respectively. The crate is

initially at rest.

a) 14.2 m/s

b) 14.7 m/s

c) 14.9 m/s

d) 14.3 m/s

Q.72 A particle is traveling along the parabolic path y = 0.25x2. If x = (2t

2) m, where t is in

seconds, determine the magnitude of the particle's velocity and acceleration when t = 2 s. a) 31 m/s & 45 m/s2

b) 32 m/s & 47.3m/s2

c) 33 m/s & 48.2m/s2

d) None of these

Q.73 Determine the speed at which the basketball at A must be thrown at the angle of 30° so that it makes it to the basket at B.

a) 12.4 m/s

b) 12.0 m/s c) 11.9 m/s d) 11.0 m/s Q.75 A projectile is fired with an initial velocity of VA = 150 m/s off the roof of the building. Determine the range R where it strikes the ground at B.

a) 2.50km b) 2.49km c) 2.55km d) 2.39km

Q.76 If the motor exerts a force of F = (600 + 2s2) N on the cable, determine the speed of the

100-kg crate when it rises to s = 15 m. The crate is initially at rest on the ground.

a) 12.0 m/s b) 12.5 m/s

c) 13.0 m/s d) 13.5 m/s Q.78 The coefficient of kinetic friction between the 20-kg block and the inclined plane is µk = 0.2. If the block is traveling up the inclined plane with a constant velocity v = 5 m/s, determine the power of force F.

a) 660W b) 630W c) 665W d) 670W Q.79 A motor hoists a 60-kg crate at a constant velocity to a height of h =5 m in 2 s. If the indicated power of the motor is 3.2 kW, determine the motor's efficiency

a) 0.360 b) 0.260 c) 0.560 d) 0.460

Q.80 The crate has a mass of 150 kg and rests on a surface for which the coefficients of static and kinetic friction are µ s = 0.3 and µk = 0.2, respectively. If the motor M supplies a cable force of F = (8t

2 + 20) N, where t is in seconds, determine the power output developed by the motor

when t = 5 s.

a) 1.15kW b) 1.12kW c) 1.18kW d) 1.20kW Q.81 If the 75-kg crate starts from rest at A, and its speed is 6 m/s when it passes point B, determine the constant force F exerted on the cable. Neglect friction and the size of the pulley.

a) 360N b) 362N c) 365N d) 367N

Q.82 The cylinder has a mass of 20 kg and is released from rest when h = 0. Determine its speed when h = 3 m. The springs each have an unstretched length of 2 m.

a) 6.66m/s b) 6.75m/s c) 6.97m/s d) 7.03m/s Q.83The 0.5-kg ball strikes the rough ground and rebounds with the velocities shown. Determine the magnitude of the impulse the ground exerts on the ball. Assume that the ball does not slip when it strikes the ground, and neglect the size of the ball and the impulse produced by the weight of the ball.

a) 12.0N.s b) 12.2N.s c) 12.4N.s d) 12.6N.s Q.84 If cylinder A is given an initial downward speed of 2 m/s, determine the speed of each cylinder when t = 3 s. Neglect the mass of the pulleys.

a) VA= VB = 1.27m/s b) VA= VB = 1.37m/s c) VA= VB = 1.47m/s d) VA= VB = 1.57m/s Q.85 At the instant the cable fails, the 200-lb crate is traveling up the plane with a speed of 15 ft/s. Determine the speed of the crate 2 s afterward. The coefficient of kinetic friction between the crate and the plane is µk= 0.20.

a) 26.4 ft/s

b) 36.4ft/s

c) 46 ft/s

d) None of these

Q.86 When the gear rotates 20 revolutions, it achieves an angular velocity of w = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required.

a) 3.12 rad/s2 & 8.0s b) 3.30 rad/s2 & 9.4s

c) 3.19 rad/s2 & 8.42s d) 3.58 rad/s

2 & 8.38s

Q.87 The bucket is hoisted by the rope that wraps around a drum wheel. If the angular displacement of the wheel is Ø = (0.5t3 + 15t) rad, where t is in seconds, determine the velocity and acceleration of the bucket when t= 3 s.

a) 21.4 ft/s & 6.75ft/s

2 b) 21.8 ft/s & 6.95ft/s2 c) 21.6 ft/s & 6.87ft/s2 d) None of these Q.88 If roller A moves to the right with a constant velocity of VA = 3 m/s, determine the angular velocity of the link and the velocity of roller B at the instant Ø = 30°.

a) w= 3 rad/s & VB=4.20m/s b) w= 4 rad/s & VB=5.20m/s

c) w= 2 rad/s & VB=3.20m/s

d) None of these Q.89 If crank OA rotates with an angular velocity of w = 12 rad/s, determine the velocity of piston B and the angular velocity of rod AB at the instant shown

a) wAB = 11 rad/s & VAB = 5.24 m/s

b) wAB = 12 rad/s & VAB = 6.24 m/s c) wAB = 13 rad/s & VAB = 7.24 m/s

d) wAB = 14 rad/s & VAB =8.24 m/s

Q.90 A bowling ball is cast on the "alley" with a backspin of w = 10 rad/s while its center O has a forward velocity of V0 = 8 m/s. Determine the velocity of the contact point A in contact with the alley.

a) 8.20m/s b) 6.20m/s c) 9.20m/s d) None Q.91 The 80-kg wheel has a radius of gyration about its mass center O of ko = 400 mm. Determine its angular velocity after it has rotated 20 revolutions starting from rest.

a) 24.3 rad/s

b) 24.6 rad/s c) 24.0 rad/s d) 23.9 rad/s Q.92 The uniform 50-kg slender rod is at rest in the position shown when P = 600 N is applied. Determine the angular velocity of the rod when the rod reaches the vertical position.

a) 2.22 rad/s b) 2.45 rad/s c) 2.50 rad/s d) 2.73 rad/s Q.93 If the system is released from rest, determine the speed of the 20-kg cylinders A and B after A has moved downward a distance of 2 m. The differential pulley has a mass of 15 kg with a radius of gyration about its center of mass of ko = 100 mm.

a) VA= 3.40m/s & VB = 1.40m/s

b) VA= 3.08m/s & VB = 1.95m/s

c) VA= 3.52m/s & VB = 1.76m/s

d) VA= 3.32m/s & VB = 1.65m/s

Q.94 A projectile is fired with a velocity of 100.3m/sec. at an elevation of 60°. The velocity attained by the projectile when it is moving at a height of 100m, is a) 90 m/sec.

b) 70 m/sec. c) 80 m/sec. d) 85 m/sec. Q.95 In a simple screw jack, the pitch of the screw is 9mm and length of the handle operating the screw is 45cm. The velocity ratio of the system is a) 1.5 b) 5 c) 25 d) 314

Q.96 A ball of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/sec hits an identical stationary ball B on the table. If the Impact is perfectly plastic, the velocity of the ball B just after impact would be a) 0 m/sec

b) 5 m/sec. c) 10 m/sec. d) None of these. Q.97 A projectile is thrown at an angle α to the horizontal with a velocity v. It will have the maximum centripetal acceleration a) at the top of the trajectory b) at the start c) as it strikes the ground d) elsewhere. Q.98 A 50 kg boy climbs up an 8 m rope in gymnasium in 10 sec. The average power developed by the boy is approximately a) 4000 watts b) 500 watts c) 400 watts

a) none of these. Q.99 A pilot flies a small plane in a vertical loop of radius r. At the top of its trajectory he experiences weightlessness. If the acceleration due to gravity is g, the speed of the plane at the top of its trajectory would be a) Zero b) infinite

c) gr

d) gr2

Q.100 The displacement of a particle which moves along a straight line is given by S = 4t

3 + 3t

2 – 10 Where S is in metres and t is in seconds. The time taken by the particle to

acquire a velocity of 18 m/sec from rest, is a) ½ sec. b) 1.5sec. c) 2.5 sec. d) 1 sec.