Question 1

A particle moves along the x axis from x_i to x_f.Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude?

Accepted Answer

The displacement is given by the difference between the final and initial coordinates. Thus, we need to choose the option with the greatest difference in absolute value. Option E gives a displacement of |-4m - 4m| = 8m, which is greater than the other options.

Question 2

You leave your house and drive to your friend's house, where you stay a while.Then you come back home.Which of the following must be true of your trip?

Accepted Answer

Your average velocity is zero because you returned to your starting point, making your total displacement zero. Average velocity is displacement divided by time, and if displacement is zero, so is average velocity.

Question 3

A particle moves along the x axis from x_i to x_f.Of the following values of the initial and final coordinates, which results in a negative displacement?

Accepted Answer

B

Question 4

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither.The time for this round trip is 2 hours.The magnitude of the average velocity of the car for this round trip is:

Accepted Answer

The average velocity is calculated as the total displacement divided by the total time. Since the car returns to its starting point, the total displacement is 0 km. Therefore, the magnitude of the average velocity is 0 km/hr, regardless of the total distance traveled or the time taken.

Question 5

The average speed of a moving object during a given interval of time is always:

Accepted Answer

The average speed of a moving object during a given interval of time is the total distance covered during that interval divided by the time interval. It does not take into account the direction of motion, which is considered in average velocity. Option A is incorrect because average velocity considers the direction of motion, and thus, the magnitude of the average velocity may be different from the average speed. Option C, D and E are incorrect because they do not represent the definition of average speed.

Question 6

This graph shows the position of a particle as a function of time.What is its average velocity between t = 5s and t = 9s?

Accepted Answer

The answer of This graph shows the position of a...

Question 7

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither.The time for this round trip is 2 hours.The average speed of the car for this round trip is:

Accepted Answer

The answer of A car starts from Hither, goes 50...

Question 8

Two automobiles are 150 kilometers apart and traveling toward each other.One automobile is moving at 60 km/h and the other is moving at 40 km/h.In how many hours will they meet?

Accepted Answer

We can use the formula: distance = rate x time
Let's call the time we are looking for "t". 
Car 1 travels a distance of (60 km/h)(t) in t hours. 
Car 2 travels a distance of (40 km/h)(t) in t hours. 
When they meet, the combined distance they travel is 150 km. 
So we can set up the equation: 
(60 km/h)(t) + (40 km/h)(t) = 150 km
Simplifying this equation gives: 
100t = 150
t = 1.5 hours. 
Therefore, the answer is D.

Question 9

This graph shows the position of a particle as a function of time.What is its instantaneous velocity at t = 7s?

Accepted Answer

The answer of This graph shows the position of a...

Question 10

The coordinate of a particle in meters is given by x(t)= 16t - 3.0t³, where the time t is in seconds.The particle is momentarily at rest at t =

Accepted Answer

To find when the particle is momentarily at rest, we need to find when its velocity is zero. The velocity is the derivative of the position function with respect to time. The given position function is $x(t) = 16t - 3.0t^{3}$. Differentiating this with respect to time gives the velocity function: $v(t) = \frac{dx}{dt} = 16 - 9t^{2}$. Setting this equal to zero to find when the particle is at rest gives $0 = 16 - 9t^{2}$, which simplifies to $9t^{2} = 16$, and further to $t^{2} = \frac{16}{9}$. Taking the square root of both sides gives $t = \pm\frac{4}{3}$, but since time cannot be negative in this context, $t = \frac{4}{3}$ seconds or 1.3 seconds.

Question 11

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

Accepted Answer

The answer of Which of the following five coordinate versus...

Question 12

Which of the following five coordinate versus time graphs represents the motion of an object moving with a constant nonzero speed?

Accepted Answer

Graph II represents an object moving with a constant nonzero speed because it has a constant positive slope, indicating a constant rate of change and therefore a constant speed. The other graphs have sections with zero slope or changing slopes, indicating changes in speed or acceleration.

Question 13

Each of four particles moves along an x axis.Their coordinates (in meters)as functions of time (in seconds)are given by  For which of these particles is the velocity increasing for t > 0?

Accepted Answer

The velocity of a particle is given by its derivative with respect to time.

Particle 1: v(t) = -3t² + 24t - 27
v'(t) = -6t + 24

v'(t) is decreasing for all t > 0, so the velocity of particle 1 is not increasing.

Particle 2: v(t) = 9t - 21
v'(t) = 9

v'(t) is constant and positive for all t > 0, so the velocity of particle 2 is increasing.

Particle 3: v(t) = 6t² - 48t + 87
v'(t) = 12t - 48

v'(t) is increasing for t > 4, so the velocity of particle 3 is increasing for t > 4.

Particle 4: v(t) = -2t³ + 24t² - 102t + 143
v'(t) = -6t² + 48t - 102

v'(t) is a quadratic function with a negative leading coefficient, so it has a maximum value at t = 4. Since v'(4) = 6, which is positive, and v'(t) is decreasing for t > 4, the velocity of particle 4 is increasing for t in the interval (0,4).

Therefore, the only particles whose velocity is increasing for t > 0 are particle 2 and particle 3. The correct answer is choice C, "Only 2 and 3."

Question 14

The position y of a particle moving along the y axis depends on the time t according to the equation y = at - bt².The dimensions of the quantities a and b are respectively:

Accepted Answer

- From the equation, y = at - bt^(2), we know that a must have the dimensions of length divided by time (L/T) because it is multiplying the time term in the equation. - We also know that b must have dimensions of length divided by time squared (L/T²) because it is multiplying the square of time in the equation. - Therefore, the best choice for the dimensions of a and b respectively are L/T and L/T², which is option C.

Question 15

A particle moves from point x₁ to point x₂.Its displacement is given by:

Accepted Answer

Displacement is the change in position of an object. Therefore, the displacement of the particle is given by the final position minus the initial position. Hence, the correct answer is x₂ - x₁.

Question 16

When can you treat a moving object as if it were a point-like particle?

Accepted Answer

To treat a moving object as a point-like particle, all parts of the object must be moving in the same direction and at the same rate. This is often the case when the object is undergoing translational motion. If the object is rotating or deforming, it cannot be treated as a point-like particle. Therefore, option A is incorrect. Option B is incorrect because not all moving objects can be treated as point-like particles. Option C is incorrect because constant acceleration is not a requirement for treating an object as a point-like particle. Option E is incorrect because the question has physical meaning.

Question 17

The coordinate-time graph of an object is a straight line with a positive slope.The object has:

Accepted Answer

A straight line with a positive slope on a coordinate-time graph represents constant velocity. Therefore, the object has a constant velocity.

Question 18

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds.Its average velocity over the interval from t = 0 to t = 2 s is:

Accepted Answer

The answer of The coordinate of an object is given...

Question 19

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds.Its velocity at t = 3s is:

Accepted Answer

To find the velocity of the object, we need to take the derivative of its position function with respect to time:

dx/dt = 7 - 3cos(t^2)

We can then evaluate this expression at t = 3s to find the velocity at that time:

dx/dt = 7 - 3cos(9)

dx/dt ≈ -11 m/s

Therefore, the answer is B.

Question 20

A car travels 40 kilometers at an average speed of 80 km/h and then travels 40 kilometers at an average speed of 40 km/h.The average speed of the car for this 80 km trip is:

Accepted Answer

The total time for the trip is the sum of the times for each segment. For the first 40 km at 80 km/h, it takes 0.5 hours. For the next 40 km at 40 km/h, it takes 1 hour. The total time is 1.5 hours for 80 km, so the average speed is 80 km / 1.5 hours = 53.33 km/h, which rounds to 53 km/h, but due to the options provided, the closest correct option based on calculation is 60 km/h, indicating a mistake in the explanation process. The correct calculation should be: Total distance = 80 km, Total time = 0.5 hours + 1 hour = 1.5 hours, Average speed = Total distance / Total time = 80 km / 1.5 hours = 53.33 km/h. Therefore, the correct answer should be C) 53 km/h, indicating an error in the initial response.

Quiz 2: Motion Along a Straight Line

A particle moves along the x axis from x_i to x_f.Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude?

You leave your house and drive to your friend's house, where you stay a while.Then you come back home.Which of the following must be true of your trip?

A particle moves along the x axis from x_i to x_f.Of the following values of the initial and final coordinates, which results in a negative displacement?

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither.The time for this round trip is 2 hours.The magnitude of the average velocity of the car for this round trip is:

The average speed of a moving object during a given interval of time is always:

This graph shows the position of a particle as a function of time.What is its average velocity between t = 5s and t = 9s?

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither.The time for this round trip is 2 hours.The average speed of the car for this round trip is:

Two automobiles are 150 kilometers apart and traveling toward each other.One automobile is moving at 60 km/h and the other is moving at 40 km/h.In how many hours will they meet?

This graph shows the position of a particle as a function of time.What is its instantaneous velocity at t = 7s?

The coordinate of a particle in meters is given by x(t) = 16t - 3.0t³, where the time t is in seconds.The particle is momentarily at rest at t =

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

Which of the following five coordinate versus time graphs represents the motion of an object moving with a constant nonzero speed?

Each of four particles moves along an x axis.Their coordinates (in meters) as functions of time (in seconds) are given by For which of these particles is the velocity increasing for t > 0?

The position y of a particle moving along the y axis depends on the time t according to the equation y = at - bt².The dimensions of the quantities a and b are respectively:

A particle moves from point x₁ to point x₂.Its displacement is given by:

When can you treat a moving object as if it were a point-like particle?

The coordinate-time graph of an object is a straight line with a positive slope.The object has:

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds.Its average velocity over the interval from t = 0 to t = 2 s is:

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds.Its velocity at t = 3s is:

A car travels 40 kilometers at an average speed of 80 km/h and then travels 40 kilometers at an average speed of 40 km/h.The average speed of the car for this 80 km trip is:

Quiz 2: Motion Along a Straight Line

A particle moves along the x axis from xi to x f .Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude?

You leave your house and drive to your friend's house, where you stay a while.Then you come back home.Which of the following must be true of your trip?

A particle moves along the x axis from xi to x f .Of the following values of the initial and final coordinates, which results in a negative displacement?

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither.The time for this round trip is 2 hours.The magnitude of the average velocity of the car for this round trip is:

The average speed of a moving object during a given interval of time is always:

This graph shows the position of a particle as a function of time.What is its average velocity between t = 5s and t = 9s?

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither.The time for this round trip is 2 hours.The average speed of the car for this round trip is:

Two automobiles are 150 kilometers apart and traveling toward each other.One automobile is moving at 60 km/h and the other is moving at 40 km/h.In how many hours will they meet?

This graph shows the position of a particle as a function of time.What is its instantaneous velocity at t = 7s?

The coordinate of a particle in meters is given by x(t) = 16t - 3.0t3, where the time t is in seconds.The particle is momentarily at rest at t =

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

Which of the following five coordinate versus time graphs represents the motion of an object moving with a constant nonzero speed?

Each of four particles moves along an x axis.Their coordinates (in meters) as functions of time (in seconds) are given by For which of these particles is the velocity increasing for t > 0?

The position y of a particle moving along the y axis depends on the time t according to the equation y = at - bt2.The dimensions of the quantities a and b are respectively:

A particle moves from point x1 to point x2.Its displacement is given by:

When can you treat a moving object as if it were a point-like particle?

The coordinate-time graph of an object is a straight line with a positive slope.The object has:

The coordinate of an object is given as a function of time by x = 7t - 3t2, where x is in meters and t is in seconds.Its average velocity over the interval from t = 0 to t = 2 s is:

The coordinate of an object is given as a function of time by x = 7t - 3t2, where x is in meters and t is in seconds.Its velocity at t = 3s is:

A car travels 40 kilometers at an average speed of 80 km/h and then travels 40 kilometers at an average speed of 40 km/h.The average speed of the car for this 80 km trip is:

A particle moves along the x axis from x_i to x_f.Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude?

A particle moves along the x axis from x_i to x_f.Of the following values of the initial and final coordinates, which results in a negative displacement?

The coordinate of a particle in meters is given by x(t) = 16t - 3.0t³, where the time t is in seconds.The particle is momentarily at rest at t =

The position y of a particle moving along the y axis depends on the time t according to the equation y = at - bt².The dimensions of the quantities a and b are respectively:

A particle moves from point x₁ to point x₂.Its displacement is given by:

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds.Its average velocity over the interval from t = 0 to t = 2 s is:

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds.Its velocity at t = 3s is: