Motion Problems: Master the Dynamics of Calculus III

Question 1

A vertically launched projectile has an initial velocity of 50 m/s. Calculate its maximum height.

Accepted Answer

127.4 m

Answer

63.7 m

Answer

254.8 m

Answer

509.6 m

Question 2

A car traveling at a constant speed of 60 mph for 3 hours will cover what distance?

Accepted Answer

270 miles

Answer

90 miles

Answer

180 miles

Answer

360 miles

Question 3

A particle's circular motion has a radius of 5 m and an angular velocity of 2 rad/s. Calculate the particle's tangential velocity.

Accepted Answer

5 m/s

Answer

2 m/s

Answer

10 m/s

Answer

20 m/s

Question 4

Identify the option that does NOT represent a type of motion problem.

Accepted Answer

Statics

Answer

Kinematics

Answer

Dynamics

Answer

Kinetics

Question 5

A 5 kg mass is subjected to a force of 100 N. Determine the resulting acceleration.

Accepted Answer

10 m/s^2

Answer

5 m/s^2

Answer

20 m/s^2

Answer

50 m/s^2

Question 6

A projectile is launched at an angle of 30 degrees above the horizontal. Calculate the horizontal component of its launch velocity.

Accepted Answer

v cos(30)

Answer

v sin(30)

Answer

v tan(30)

Answer

v sec(30)

Question 7

Identify the unit of angular acceleration.

Accepted Answer

rad/s^2

Answer

m/s^2

Answer

m/s

Answer

rad/s

Question 8

A spring has a natural length of 10 centimeters. When a force of 5 Newtons is applied to the spring, it stretches to a length of 15 centimeters. What is the spring constant?

Accepted Answer

5 Newtons per centimeter

Answer

10 Newtons per centimeter

Answer

15 Newtons per centimeter

Answer

20 Newtons per centimeter

Question 9

A particle moves along a straight line with an initial velocity of 2 m/s. Its acceleration is given by a(t) = t - 2. Determine the particle's displacement after 5 seconds.

Accepted Answer

12.5 m

Answer

5 m

Answer

2.5 m

Question 10

A car travels north at 60 mph. A plane travels east at 100 mph. What is the plane's velocity relative to the car?

Accepted Answer

40 mph, 63.4° east of north

Answer

160 mph, 45° east of north

Answer

40 mph, 26.6° west of north

Question 11

A particle of mass m moves in a circular path of radius r with constant speed v. What is the magnitude of the centripetal force acting on the particle?

Accepted Answer

mv²/r

Answer

2mv²/r

Answer

mv²/2r

Answer

mg

Question 12

A car travels 60 miles in 1.5 hours. What is the car's average velocity?

Accepted Answer

40 mph

Answer

25 mph

Answer

55 mph

Answer

70 mph

Question 13

A particle moves along the curve y = x³. What is the particle's acceleration vector at the point (1, 1)?

Accepted Answer

(3, 3)

Answer

(3, -3)

Answer

(-3, 3)

Answer

(-3, -3)

Question 14

A car is traveling along a straight highway at a constant speed of 50 mi/h. If the car's distance from a fixed point is given by s(t) = 50t, what is its acceleration?

Accepted Answer

0

Answer

50

Answer

100

Answer

200

Question 15

A ball is thrown horizontally from a height of 10 m with an initial velocity of 20 m/s. What is the range of the ball?

Accepted Answer

40 m

Answer

20 m

Answer

60 m

Answer

80 m

Question 16

An object is thrown vertically upward with an initial velocity of 20 m/s from a height of 10 meters. What maximum height will it reach?

Accepted Answer

25 meters

Answer

15 meters

Answer

35 meters

Answer

10 meters

Question 17

A force of 10 Newtons is applied to a stationary object of mass 2 kilograms. What is the object's acceleration?

Accepted Answer

5 meters per second squared

Answer

2 meters per second squared

Answer

10 meters per second squared

Question 18

A car travels 100 kilometers in 1 hour and 30 minutes. What is the car's average speed in kilometers per hour?

Accepted Answer

67 kilometers per hour

Answer

50 kilometers per hour

Answer

75 kilometers per hour

Answer

100 kilometers per hour

Question 19

A car is traveling around a circular track of radius 100 m. If the car's angular velocity is 2 rad/s, what is its linear velocity (in m/s)?

Accepted Answer

200 m/s

Answer

400 m/s

Answer

100 m/s

Answer

300 m/s

Question 20

A missile is launched with an initial velocity of 300 m/s at an angle of 30° with respect to the horizontal. What is the horizontal range of the missile?

Accepted Answer

3464 m

Answer

4500 m

Answer

1500 m

Answer

2200 m

Question 21

A car travels around a curve with a radius of 50 m at a constant speed of 15 m/s. What is the car's angular acceleration?

Accepted Answer

0.3 rad/s^2

Answer

0.45 rad/s^2

Answer

0.6 rad/s^2

Answer

0.15 rad/s^2

Question 22

A block of mass 2 kg is attached to a spring with a spring constant of 100 N/m. The block is displaced 0.1 m to the right of its equilibrium position and released. What is the amplitude of the block's motion?

Accepted Answer

0.1 m

Answer

0.05 m

Answer

0.2 m

Question 23

A particle moves in a circle of radius 2 m with a constant tangential velocity of 10 m/s. What is the particle's centripetal acceleration?

Accepted Answer

50 m/s^2

Answer

25 m/s^2

Answer

100 m/s^2

Answer

75 m/s^2

Question 24

A rocket of mass 1000 kg burns fuel at a rate of 2 kg/s. The exhaust velocity relative to the rocket is 1500 m/s. What is the rocket's acceleration?

Accepted Answer

30 m/s^2

Answer

20 m/s^2

Answer

15 m/s^2

Answer

45 m/s^2

Question 25

A ball is thrown vertically upward with an initial velocity of 20 m/s. What is the maximum height reached by the ball?

Accepted Answer

20.4 m

Answer

10.2 m

Answer

30.6 m

Answer

15.3 m

Question 26

A car travels a distance of 100 km in 2 hours. What is the car's average velocity?

Accepted Answer

50 km/h

Answer

25 km/h

Answer

75 km/h

Question 27

A block slides down an inclined plane with an angle of inclination of 30°. The coefficient of kinetic friction between the block and the plane is 0.2. What is the acceleration of the block?

Accepted Answer

4.9 m/s^2

Answer

7.35 m/s^2

Answer

9.8 m/s^2

Answer

2.45 m/s^2

Question 28

A simple pendulum of length 1 m has a mass of 0.5 kg. What is the period of oscillation?

Accepted Answer

2π s

Answer

4π s

Answer

3π s

Answer

π s

Question 29

A ball is thrown horizontally from a height of 10 m with an initial velocity of 15 m/s. What is the range of the ball?

Accepted Answer

22.5 m

Answer

20 m

Answer

15 m

Answer

30 m