Question 1

The area under a graph of v_x vs.t from t = t_i to t = t_f represents

Accepted Answer

The area under a graph represents the integral of the function over the specified interval. Thus, the area under v_x vs.t from t = t_i to t = t_f represents the integral of v_x with respect to t over the interval t = t_i to t = t_f. This integral can be written as ∫v_x dt from t = t_i to t = t_f. The answer is, therefore, C) x_f F1F1F1S1F1F1F10 x_i.

Question 2

A bullet is fired through a board,14.0 cm thick,with its line of motion perpendicular to the face of the board.If it enters with a speed of 450 m/s and emerges with a speed of 220 m/s,what is the bullet's acceleration as it passes through the board?

Accepted Answer

B

Question 3

A particle is moving at constant velocity.Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m.What is the slope of the position-time graph for this particle?

Accepted Answer

The slope of the position-time graph represents the velocity of the particle. To find the slope (velocity) = (change in position) / (change in time) = (15.0 m - 3.0 m) / (4.0 s - 1.0 s) = 12 m / 3 s = 4.0 m/s.

Question 4

The position of a particle as it moves along the x axis is given by x = 15e ^- ²^t m,where t is in s.What is the acceleration of the particle at t = 1.0 s?

Accepted Answer

Taking the second derivative of x with respect to t will give us the acceleration, so:

x = 15e^(t-sin(pi/2)t+ln(10)) 
v = dx/dt = 15e^(t-sin(pi/2)t+ln(10))(1-cos(pi/2)) = 15e^(t-sin(pi/2)t+ln(10))sin(pi/2) = 15e^(t-sin(pi/2)t+ln(10)) 
a = dv/dt = 15e^(t-sin(pi/2)t+ln(10))(1-cos(pi/2)) = 15e^(t-sin(pi/2)t+ln(10))(pi/2)cos(pi/2) = 8.1 m/s^2

Therefore, the acceleration of the particle at t = 1.0 s is 8.1 m/s^2.

The correct answer is C.

Question 5

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below.Which statement is correct?

Accepted Answer

In diagram D, the points become farther apart and then closer together, indicating a change in speed. The object is therefore accelerating, starting from rest and increasing in speed before decelerating back to rest. A has a constant speed, B has a negative constant velocity (moving to the left), C has a constant velocity but decreasing speed, and E has a greater constant speed than A, but there is no indication of acceleration.

Question 6

A car travels north at 30 m/s for one half hour.It then travels south at 40 m/s for 15 minutes.The total distance the car has traveled and its displacement are:

Accepted Answer

First, we need to convert the given time values to seconds to match the units of speed:

- The first half hour of travel is 0.5 hours x 60 minutes/hour x 60 seconds/minute = 1800 seconds.
- The second 15 minutes of travel is 0.25 hours x 60 minutes/hour x 60 seconds/minute = 900 seconds.

Next, we can use the formula:

distance = speed x time

to calculate the distance traveled in each direction. Note that the northward distance will be positive and the southward distance will be negative.

- Distance traveled north = 30 m/s x 1800 s = 54,000 m = 54 km
- Distance traveled south = -40 m/s x 900 s = -36,000 m = -36 km

The total distance traveled is the sum of the magnitudes of these two distances:

|54 km| + |-36 km| = 54 km + 36 km = 90 km

Finally, the displacement is the net distance traveled in a straight line from the initial position to the final position. Since the car ends up north of its starting point, the displacement is positive and northward:

displacement = |54 km - 36 km| = 18 km (north)

Question 7

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals.Assume the body moves in a straight line.  This diagram is most likely to describe

Accepted Answer

The diagram shows a back-and-forth motion, with the body moving forward, stopping abruptly, and then moving in the opposite direction. This is most likely to occur if a runner trips, falls, gets up quickly, and continues racing. The other options (swimming laps, rowing machine, treadmill, and tennis ball volley) would show a more repetitive, cyclical motion.

Question 8

A particle moving along the x axis has a position given by x = 54t -2.0t³ m.At the time t = 3.0 s,the speed of the particle is zero.Which statement is correct?

Accepted Answer

The speed of the particle is zero at t = 3.0 s, but it does not imply the particle remains at rest or stops accelerating after this time. The particle's position can be negative for positive t values, depending on the equation.

Question 9

In 20 minutes,Kara ran 2.40 km on a treadmill facing due east.Relative to the gym,what were her displacement and average velocity during this time interval?

Accepted Answer

The answer of In 20 minutes,Kara ran 2.40 km on...

Question 10

Driver A is cruising along enjoying the fall colors.Driver B starts her car at the instant he passes her.Their velocities are shown as functions of time in the graph below.At what instants in time on the graph are drivers A and B side by side?

Accepted Answer

The answer of Driver A is cruising along enjoying the...

Question 11

A particle moving with a constant acceleration has a velocity of 20 cm/s when its position is x = 10 cm.Its position 7.0 s later is x = -30 cm.What is the acceleration of the particle?

Accepted Answer

Explanation:The equation of motion is:v = u + atwhere v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.We are given that v = 20 cm/s, u = 0 cm/s (since the particle starts from rest), t = 7.0 s, and x = 30 cm.We can use the equation of motion to find the acceleration:a = (v - u) / t= (20 cm/s - 0 cm/s) / 7.0 s= 2.86 cm/s^2Therefore, the acceleration of the particle is 2.86 cm/s^2.

Question 12

Two children start at one end of a street,the origin,run to the other end,then head back.On the way back Joan is ahead of Mike.Which statement is correct about the distances run and the displacements from the origin?

Accepted Answer

Since Joan was ahead of Mike on the way back, this means that she must have run further than him during that portion of the run. Therefore, option A and B are incorrect. However, because the starting point is also the ending point, the total displacement for both runners is zero. Therefore, option C is correct as it states that Joan has run a greater distance (during the second half of the run), but her displacement is less than Mike's (which is also zero). Options D and E are also incorrect as they state that Mike has run a greater distance, which is not necessarily true based on the information given.

Question 13

A particle moving along the x axis has a position given by x = (24t - 2.0t³)m,where t is measured in s.What is the magnitude of the acceleration of the particle at the instant when its velocity is zero?

Accepted Answer

The acceleration of the particle is the second derivative of its position with respect to time. The given position function is x = 24t - 2.0t^3. The first derivative, which gives the velocity, is v = dx/dt = 24 - 6t^2. Setting this equal to zero to find when the velocity is zero gives 24 - 6t^2 = 0, solving for t gives t = 2 seconds. The second derivative, which gives the acceleration, is a = d^2x/dt^2 = -12t. Substituting t = 2 seconds into the acceleration equation gives a = -12(2) = -24 m/s^2. The magnitude of the acceleration is 24 m/s^2, indicating choice A is correct.

Question 14

A proton moving along the x axis has an initial velocity of 4.0 * 10⁶ m/s and a constant acceleration of 6.0*10¹² m/s².What is the velocity of the proton after it has traveled a distance of 80 cm?

Accepted Answer

Explanation:The velocity of the proton after it has traveled a distance of 80 cm is given by:$$v^2 = u^2 + 2as$$where:* v is the final velocity* u is the initial velocity* a is the acceleration* s is the distance traveledSubstituting the given values into the equation, we get:$$v^2 = (4.0 	imes 10^6 \ m/s)^2 + 2(6.0 	imes 10^{12} \ m/s^2)(0.80 \ m)$$$$v^2 = 1.60 	imes 10^{13} \ m^2/s^2$$$$v = 4.0 	imes 10^6 \ m/s$$Therefore, the velocity of the proton after it has traveled a distance of 80 cm is 4.0 × 10^6 m/s.

Question 15

A swimmer swims 20 laps in a north-south facing pool in 7.00 minutes.Her first lap is toward the north.Her displacement and average velocity are

Accepted Answer

Displacement is a vector quantity that refers to the change in position of an object. Since the swimmer returns to the starting point after completing an even number of laps in a north-south facing pool, the overall change in position is zero, making the displacement 0. Average velocity is displacement divided by time. Since the displacement is 0, the average velocity is also 0, regardless of the distance swum or the time taken.

Question 16

The position of an object at equal time intervals is shown below:  Which graph below correctly represents position versus time for this object?

Accepted Answer

The answer of The position of an object at equal...

Question 17

A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5-s time interval.The velocity of the particle at x = 8.0 m is 2.8 m/s.What is the acceleration during this time interval?

Accepted Answer

To find the acceleration, we can use the formula $v_f = v_i + at$, where $v_f$ is the final velocity, $v_i$ is the initial velocity, $a$ is the acceleration, and $t$ is the time. We are not directly given $v_i$, but we can find it using the displacement formula $x = x_0 + v_i t + \frac{1}{2}at^2$, where $x$ is the final position, $x_0$ is the initial position, and the other symbols have their usual meanings. Substituting the given values into the displacement formula, we can solve for $v_i$, and then use the first formula to solve for $a$. However, without the initial velocity, we cannot directly solve for acceleration using the given information alone. The correct approach involves using both the given displacement and the final velocity to find acceleration, but the provided information and method in the explanation are insufficient to directly arrive at the correct answer without the initial velocity or a more detailed calculation. Therefore, a mistake was made in the explanation process. To correctly solve for acceleration, one would typically use the kinematic equations, taking into account the total displacement and the time taken, but the direct calculation from the initial setup was not provided.

Question 18

The position of a particle moving along the x axis is given by x = (21 + 22t -6.0t²)m,where t is in s.What is the average velocity during the time interval t = 1.0 s to t = 3.0 s?

Accepted Answer

To find the average velocity during the time interval from t = 1.0 s to t = 3.0 s, we need to find the displacement of the particle during this time interval and divide it by the time interval.

The displacement of the particle between t = 1.0 s and t = 3.0 s is:

x(3) - x(1) = [(21 + 22(3)) - (21 + 22(1))] m = 44 m

The time interval is:

Δt = 3.0 s - 1.0 s = 2.0 s

Therefore, the average velocity is:

v = Δx/Δt = 44 m/2.0 s = 22 m/s

The correct answer should be in m/s, so we can eliminate choices A, B, and D, which have units of m/s^2, and also choice E, which has a value of 8.0 m/s, which is not equal to the calculated value of 22 m/s. Therefore, the best choice is C, which has a value of 2.0 m/s.

Question 19

To help Kim practice for the Special Olympics,Sally runs beside him for half the required distance.She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim.What is the ratio of Sally's regular speed to Kim's speed? Use t_Kim for Kim's total time.

Accepted Answer

The answer of To help Kim practice for the Special...

Question 20

The position of a particle moving along the y axis has a position given by $y = 0.20 \mathrm {~m} + \left( 8.0 \frac { \mathrm { m } } { \mathrm { s } } \right) t - \left( 10 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) t ^ { 2 }$ Is there any time interval during which the particle is not moving?

Accepted Answer

The answer of The position of a particle moving along...

Quiz 2: Motion in One Dimension

The area under a graph of v_x vs.t from t = t_i to t = t_f represents

A bullet is fired through a board,14.0 cm thick,with its line of motion perpendicular to the face of the board.If it enters with a speed of 450 m/s and emerges with a speed of 220 m/s,what is the bullet's acceleration as it passes through the board?

A particle is moving at constant velocity.Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m.What is the slope of the position-time graph for this particle?

The position of a particle as it moves along the x axis is given by x = 15e ^- ²^t m,where t is in s.What is the acceleration of the particle at t = 1.0 s?

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below.Which statement is correct?

A car travels north at 30 m/s for one half hour.It then travels south at 40 m/s for 15 minutes.The total distance the car has traveled and its displacement are:

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals.Assume the body moves in a straight line. This diagram is most likely to describe

A particle moving along the x axis has a position given by x = 54t -2.0t³ m.At the time t = 3.0 s,the speed of the particle is zero.Which statement is correct?

In 20 minutes,Kara ran 2.40 km on a treadmill facing due east.Relative to the gym,what were her displacement and average velocity during this time interval?

Driver A is cruising along enjoying the fall colors.Driver B starts her car at the instant he passes her.Their velocities are shown as functions of time in the graph below.At what instants in time on the graph are drivers A and B side by side?

A particle moving with a constant acceleration has a velocity of 20 cm/s when its position is x = 10 cm.Its position 7.0 s later is x = -30 cm.What is the acceleration of the particle?

Two children start at one end of a street,the origin,run to the other end,then head back.On the way back Joan is ahead of Mike.Which statement is correct about the distances run and the displacements from the origin?

A particle moving along the x axis has a position given by x = (24t - 2.0t³) m,where t is measured in s.What is the magnitude of the acceleration of the particle at the instant when its velocity is zero?

A proton moving along the x axis has an initial velocity of 4.0 * 10⁶ m/s and a constant acceleration of 6.0*10¹² m/s².What is the velocity of the proton after it has traveled a distance of 80 cm?

A swimmer swims 20 laps in a north-south facing pool in 7.00 minutes.Her first lap is toward the north.Her displacement and average velocity are

The position of an object at equal time intervals is shown below: Which graph below correctly represents position versus time for this object?

A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5-s time interval.The velocity of the particle at x = 8.0 m is 2.8 m/s.What is the acceleration during this time interval?

The position of a particle moving along the x axis is given by x = (21 + 22t -6.0t²) m,where t is in s.What is the average velocity during the time interval t = 1.0 s to t = 3.0 s?

To help Kim practice for the Special Olympics,Sally runs beside him for half the required distance.She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim.What is the ratio of Sally's regular speed to Kim's speed? Use t_Kim for Kim's total time.

Quiz 2: Motion in One Dimension

The area under a graph of vx vs.t from t = ti to t = tf represents

A bullet is fired through a board,14.0 cm thick,with its line of motion perpendicular to the face of the board.If it enters with a speed of 450 m/s and emerges with a speed of 220 m/s,what is the bullet's acceleration as it passes through the board?

A particle is moving at constant velocity.Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m.What is the slope of the position-time graph for this particle?

The position of a particle as it moves along the x axis is given by x = 15e - 2t m,where t is in s.What is the acceleration of the particle at t = 1.0 s?

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below.Which statement is correct?

A car travels north at 30 m/s for one half hour.It then travels south at 40 m/s for 15 minutes.The total distance the car has traveled and its displacement are:

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals.Assume the body moves in a straight line. This diagram is most likely to describe

A particle moving along the x axis has a position given by x = 54t -2.0t3 m.At the time t = 3.0 s,the speed of the particle is zero.Which statement is correct?

In 20 minutes,Kara ran 2.40 km on a treadmill facing due east.Relative to the gym,what were her displacement and average velocity during this time interval?

Driver A is cruising along enjoying the fall colors.Driver B starts her car at the instant he passes her.Their velocities are shown as functions of time in the graph below.At what instants in time on the graph are drivers A and B side by side?

A particle moving with a constant acceleration has a velocity of 20 cm/s when its position is x = 10 cm.Its position 7.0 s later is x = -30 cm.What is the acceleration of the particle?

Two children start at one end of a street,the origin,run to the other end,then head back.On the way back Joan is ahead of Mike.Which statement is correct about the distances run and the displacements from the origin?

A particle moving along the x axis has a position given by x = (24t - 2.0t3) m,where t is measured in s.What is the magnitude of the acceleration of the particle at the instant when its velocity is zero?

A proton moving along the x axis has an initial velocity of 4.0 * 106 m/s and a constant acceleration of 6.0*1012 m/s2.What is the velocity of the proton after it has traveled a distance of 80 cm?

A swimmer swims 20 laps in a north-south facing pool in 7.00 minutes.Her first lap is toward the north.Her displacement and average velocity are

The position of an object at equal time intervals is shown below: Which graph below correctly represents position versus time for this object?

A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5-s time interval.The velocity of the particle at x = 8.0 m is 2.8 m/s.What is the acceleration during this time interval?

The position of a particle moving along the x axis is given by x = (21 + 22t -6.0t2) m,where t is in s.What is the average velocity during the time interval t = 1.0 s to t = 3.0 s?

To help Kim practice for the Special Olympics,Sally runs beside him for half the required distance.She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim.What is the ratio of Sally's regular speed to Kim's speed? Use tKim for Kim's total time.

The area under a graph of v_x vs.t from t = t_i to t = t_f represents

The position of a particle as it moves along the x axis is given by x = 15e ^- ²^t m,where t is in s.What is the acceleration of the particle at t = 1.0 s?

A particle moving along the x axis has a position given by x = 54t -2.0t³ m.At the time t = 3.0 s,the speed of the particle is zero.Which statement is correct?

A particle moving along the x axis has a position given by x = (24t - 2.0t³) m,where t is measured in s.What is the magnitude of the acceleration of the particle at the instant when its velocity is zero?

A proton moving along the x axis has an initial velocity of 4.0 * 10⁶ m/s and a constant acceleration of 6.0*10¹² m/s².What is the velocity of the proton after it has traveled a distance of 80 cm?

The position of a particle moving along the x axis is given by x = (21 + 22t -6.0t²) m,where t is in s.What is the average velocity during the time interval t = 1.0 s to t = 3.0 s?

To help Kim practice for the Special Olympics,Sally runs beside him for half the required distance.She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim.What is the ratio of Sally's regular speed to Kim's speed? Use t_Kim for Kim's total time.