Question 1

What is the difference between speed and velocity?
A)Speed is the magnitude of velocity; velocity is a vector and has both magnitude and direction.
B)There is no difference.
C)Speed is the rate at which something moves, while velocity is the direction in which it moves.
D)Speed is used when describing motion in one dimension, while velocity is used when describing motion in two dimensions.
E)Speed is the rate at which velocity changes.

Accepted Answer

Speed is a scalar quantity that refers to how fast an object is moving, while velocity is a vector quantity that includes both the speed and direction of the object's motion.

Question 2

Which of the following is a vector quantity?
A)Mass
B)Density
C)Speed
D)Temperature
E)None of these

Accepted Answer

Mass, density, speed, and temperature are all scalar quantities because they do not include direction in their measurement. Vector quantities require both magnitude and direction.

Question 3

Two bodies are falling with negligible air resistance, side by side, above a horizontal plane.If one of the bodies is given an additional horizontal acceleration during its descent, it:
A)strikes the plane at the same time as the other body
B)strike the plane earlier than the other body
C)has the vertical component of its velocity altered
D)has the vertical component of its acceleration altered
E)follows a straight line path along the resultant acceleration vector

Accepted Answer

The additional horizontal acceleration does not affect the vertical motion due to gravity, so both bodies hit the ground at the same time. Horizontal and vertical motions are independent in projectile motion.

Question 4

An object moves from x = -2.1 m, y = 3.7 m, z = 1.4 m to x = 3.3 m, y = -1.1 m, z = 4.2 m in a time of 5.3 s.What is its average velocity?
A)(0.23 m/s)  + (0.49 m/s)
 + (0.53 m/s)

B)(5.4 m/s)  − (4.8 m/s)
 + (2.8 m/s)

C)(1.0 m/s)  − (0.91 m/s)
 + (0.53 m/s)

D)(1.0 m/s)  + (0.91 m/s)
 + (1.1 m/s)

E)−(1.0 m/s)  + (0.91 m/s)
 + (0.53 m/s)

Accepted Answer

Average velocity is the displacement divided by the elapsed time. The final position vector minus the initial position vector gives the displacement vector.

Displacement vector = (3.3-(-2.1))i + (-1.1-3.7)j + (4.2-1.4)k 
= 5.4i - 4.8j + 2.8k

Elapsed time = 5.3 s

Average velocity = Displacement vector / elapsed time 
= (5.4/5.3)i - (4.8/5.3)j + (2.8/5.3)k 
= 1.0i - 0.91j + 0.53k

Therefore, the correct choice is C, which represents the average velocity vector as 1.0 m/s eastward (i-direction), 0.91 m/s southward (j-direction), and 0.53 m/s upward (k-direction).

Question 5

From your window you can see a high-rise building several blocks away.You check the map and see that the building is 560 m away from you in a straight line, in a direction 30° south of east.However, the roads are all east-west and north-south.If you want to walk from your house to the building, how far in each direction do you have to walk?
A)480 m east and 280 m south
B)280 m east and 480 m south
C)280 m east and 280 m south
D)480 m east and 50 m south
E)cannot be determined without looking at the streets on the map

Accepted Answer

To get to the building, we need to break down the 560m distance into its eastward and southward components. We know that the building is 30° south of east, which means that the angle between the straight-line distance and the eastward direction is 30°. Using trigonometry, we can find the eastward and southward components as follows:

Eastward distance = 560m * cos(30°) = 485m (rounded to the nearest whole number)
Southward distance = 560m * sin(30°) = 280m (rounded to the nearest whole number)

Since the roads are all east-west and north-south, we need to walk 485m east and 280m south to reach the building. Therefore, the best choice is A) 480m east and 280m south.

Question 6

A plane traveling north at 200 m/s turns and then travels south at 200 m/s.The change in its velocity is:
A)0 m/s
B)200 m/s north
C)200 m/s south
D)400 m/s north
E)400 m/s south

Accepted Answer

The change in velocity is calculated by subtracting the initial velocity from the final velocity. Since the plane initially travels north at 200 m/s and then south at 200 m/s, the change in velocity is 400 m/s to the south, considering north and south as opposite directions.

Question 7

Which of the following is a scalar quantity?
A)Speed
B)Velocity
C)Displacement
D)Acceleration
E)None of these

Accepted Answer

Speed is a scalar quantity because it only has magnitude (in this case, the magnitude is how fast an object is moving), but not direction. Velocity, displacement, and acceleration are all vector quantities because they have both magnitude and direction.

Question 8

An object has a velocity of (5.4 m/s)  − (4.8 m/s)  .Over a period of 1.3 s, its velocity changes to (1.7 m/s)  + (5.9 m/s)  .What is its acceleration?
A)−(3.7 m/s)  + (11 m/s)

B)−(2.8 m/s)  + (8.2 m/s)

C)(3.7 m/s)  + (11 m/s)

D)(2.8 m/s)  + (8.2 m/s)

E)−(2.8 m/s)  + (1.1 m/s)

Accepted Answer

The answer of An object has a velocity of (5.4...

Question 9

Sally starts from home, walks 300 m east and then 500 m south, and arrives at her school.How far, in a straight line, is Sally's school from her home?
A)300 m
B)500 m
C)580 m
D)640 m
E)800 m

Accepted Answer

Using the Pythagorean theorem, the distance between Sally's home and school can be found:
$distance = \sqrt{(300	ext{ m})^2 + (500	ext{ m})^2}$
$distance = \sqrt{90000	ext{ m}^2 + 250000	ext{ m}^2}$
$distance = \sqrt{340000	ext{ m}^2}$
$distance = 580	ext{ m}$
So Sally's school is 580 meters from her home. Answer choice C is correct.

Question 10

The position of an object as a function of time is given in meters by x = (at + bt²) + (ct) .What is its velocity as a function of time? A)v = (a + b) + (c) B)v = (a + 2b) + (c) C)v = (a + 2bt) + (c) D)v = b E)v = 2b

Accepted Answer

Velocity is the derivative of position with respect to time. 
Taking the derivative of x with respect to t, we get:
v = a + 2bt + c 
which matches with option C.

Question 11

A jet plane in straight horizontal flight passes over your head.When it is directly above you, the sound seems to come from a point behind the plane in a direction 30 $\degree$ from the vertical.The speed of the plane is:
A)the same as the speed of sound
B)half the speed of sound
C)three-fifths the speed of sound
D)0.866 times the speed of sound
E)twice the speed of sound

Accepted Answer

The answer of A jet plane in straight horizontal flight...

Question 12

Acceleration is defined as:
A)rate of change of position with time
B)speed divided by time
C)rate of change of velocity with time
D)a speeding up or slowing down
E)change of velocity

Accepted Answer

Acceleration is the rate of change of velocity with time. This means that if an object is changing its speed or direction, it is accelerating. It is not simply the rate of change of position, as an object could be moving at a constant speed but still be accelerating if it is changing direction. It is also not just speed divided by time, as this only gives the average speed and doesn't take into account any changes in velocity. Finally, acceleration can refer to both speeding up or slowing down, as long as there is a change in velocity.

Question 13

The velocity of an object as a function of time is given by v = (12.5t − 7.2t²) + (4.3t³) .What is its acceleration as a function of time? A)a = (12.5 − 14.4t) + (12.9t²) B)a = (−7.2) + (4.3t) C)a = (5.3t) + (12.9t²) D)a = (−7.2) + (8.6t) E)a = (−14.4t) + (4.3t²)

Accepted Answer

To find the acceleration as a function of time, we need to take the derivative of velocity with respect to time:

a = dv/dt

a = d/dt [ (12.5t − 7.2t^2) + (4.3t) ]

a = (12.5 − 14.4t) + 4.3

Simplifying the expression, we get:

a = (12.5 − 14.4t) + 4.3

a = 5.3t − 13.2

Therefore, the correct choice is A.

Question 14

Velocity is defined as:
A)rate of change of position with time
B)position divided by time
C)rate of change of acceleration with time
D)a speeding up or slowing down
E)change of position

Accepted Answer

Velocity is the rate of change of position with time, so option A is the best choice. Option B is incorrect because position divided by time is actually average speed, not velocity. Option C is incorrect because acceleration is the rate of change of velocity, not the other way around. Option D is incorrect because speeding up or slowing down refers to a change in velocity, not velocity itself. Option E is also incorrect because change of position can refer to distance, but velocity specifically refers to the rate of change of that position.

Question 15

A particle goes from x = -2 m, y = 3 m, z = 1 m to x = 3 m, y = -1 m, z = 4 m.Its displacement is:
A)(1 m)  + (2 m)
 + (5 m)

B)(5 m)  − (4 m)
 + (3 m)

C)−(5 m)  + (4 m)
 − (3 m)

D)−(1 m)  − (2 m)
 − (5 m)

E)−(5 m)  − (2 m)
 − (3 m)

Accepted Answer

The answer of A particle goes from x = -2...

Question 16

An object is at rest at x = 0 m, y = 0 m.It accelerates at a rate of (−3.2 m/s²) + (8.6 m/s²) .After accelerating for 4.7 seconds its coordinates are: A)x = −15 m, y = 40 m B)x = −35 m, y = 95 m C)x = −24 m, y = 170 m D)x = −70 m, y = 190 m E)x = −48 m, y = 340 m

Accepted Answer

The motion can be divided into x and y components as:
ax = -3.2 m/s^2
ay = 8.6 m/s^2

Using the equations of motion:
x = ut + 1/2 at^2
y = vt + 1/2 at^2

At t = 4.7 s,
x = 0 + 1/2 (-3.2) (4.7)^2 = -35 m
y = 0 + 1/2 (8.6) (4.7)^2 = 95 m

Therefore, the object's coordinates after 4.7 seconds are x = -35 m and y = 95 m, which matches with option B.

Question 17

The velocity of a projectile equals its initial velocity added to:
A)a constant horizontal velocity
B)a constant vertical velocity
C)a constantly increasing horizontal velocity
D)a constantly increasing downward velocity
E)a constant velocity directed at the target

Accepted Answer

The velocity of a projectile changes due to gravity, which constantly increases its downward velocity. Horizontal velocity remains constant if air resistance is neglected.

Question 18

Which of the following is NOT an example of accelerated motion?
A)Vertical component of projectile motion
B)Circular motion at constant speed
C)A swinging pendulum
D)Earth's motion about sun
E)Horizontal component of projectile motion

Accepted Answer

The horizontal component of projectile motion is not an example of accelerated motion because it remains constant if air resistance is neglected. Acceleration occurs in the vertical direction due to gravity, but not horizontally.

Question 19

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon.Which of the following three statements is/are true? I.The horizontal distance traveled by the bullet is greater for the Moon.
II.The flight time is less for the bullet on the Earth.
III.The velocities of the bullets at impact are the same.
A)III only
B)I and II only
C)I and III only
D)II and III only
E)I, II, III

Accepted Answer

The bullet on the Moon will travel a greater horizontal distance due to the lower gravitational acceleration, resulting in a longer flight time. The bullet on Earth will have a shorter flight time due to higher gravity. The velocities at impact will differ because the vertical component of velocity will be greater on Earth due to higher gravity.

Question 20

An object moves from x = -2.1 m, y = 3.7 m to x = 3.3 m, y = -1.1 m in a time of 5.3 s.What is its average velocity?
A)7.2 m/s, 32° below the positive x-axis
B)2.5 m/s, 48° below the positive x-axis
C)1.4 m/s, 42° below the positive x-axis
D)4.9 m/s, 76° below the positive x-axis
E)0.92 m/s, 14° below the positive x-axis

Accepted Answer

The average velocity is calculated by finding the displacement vector and dividing by the time. The displacement is (3.3 - (-2.1), -1.1 - 3.7) = (5.4, -4.8). The magnitude of this vector is √(5.4² + (-4.8)²) = 7.2 m. The average velocity is 7.2 m / 5.3 s = 1.4 m/s. The angle is tan⁻¹(4.8/5.4) = 42° below the positive x-axis.

Quiz 4: Motion in Two and Three Dimensions

What is the difference between speed and velocity?

Which of the following is a vector quantity?

Two bodies are falling with negligible air resistance, side by side, above a horizontal plane.If one of the bodies is given an additional horizontal acceleration during its descent, it:

An object moves from x = -2.1 m, y = 3.7 m, z = 1.4 m to x = 3.3 m, y = -1.1 m, z = 4.2 m in a time of 5.3 s.What is its average velocity?

A plane traveling north at 200 m/s turns and then travels south at 200 m/s.The change in its velocity is:

Which of the following is a scalar quantity?

An object has a velocity of (5.4 m/s) − (4.8 m/s) .Over a period of 1.3 s, its velocity changes to (1.7 m/s) + (5.9 m/s) .What is its acceleration?

Sally starts from home, walks 300 m east and then 500 m south, and arrives at her school.How far, in a straight line, is Sally's school from her home?

The position of an object as a function of time is given in meters by x = (at + bt2) + (ct) .What is its velocity as a function of time?

A jet plane in straight horizontal flight passes over your head.When it is directly above you, the sound seems to come from a point behind the plane in a direction 30 °\degree° from the vertical.The speed of the plane is:

Acceleration is defined as:

The velocity of an object as a function of time is given by v = (12.5t − 7.2t2) + (4.3t3) .What is its acceleration as a function of time?

Velocity is defined as:

A particle goes from x = -2 m, y = 3 m, z = 1 m to x = 3 m, y = -1 m, z = 4 m.Its displacement is:

An object is at rest at x = 0 m, y = 0 m.It accelerates at a rate of (−3.2 m/s2) + (8.6 m/s2) .After accelerating for 4.7 seconds its coordinates are:

The velocity of a projectile equals its initial velocity added to:

Which of the following is NOT an example of accelerated motion?

An object moves from x = -2.1 m, y = 3.7 m to x = 3.3 m, y = -1.1 m in a time of 5.3 s.What is its average velocity?

The position of an object as a function of time is given in meters by x = (at + bt²) + (ct) .What is its velocity as a function of time?

A jet plane in straight horizontal flight passes over your head.When it is directly above you, the sound seems to come from a point behind the plane in a direction 30 $\degree$ from the vertical.The speed of the plane is:

The velocity of an object as a function of time is given by v = (12.5t − 7.2t²) + (4.3t³) .What is its acceleration as a function of time?

An object is at rest at x = 0 m, y = 0 m.It accelerates at a rate of (−3.2 m/s²) + (8.6 m/s²) .After accelerating for 4.7 seconds its coordinates are: