Kaplan Physics Chapter One

Rusev started on an xy-plane at (-0.5, 3). He walks so that his final position is (-0.5, -3). What is Rusev's displacement?

(A) -6 units Displacement = Final Position - Initial Position = Net Distance (in some direction) X-displacement = -0.5 - (-0.5) = 0 Y-displacement = (-3) - 3 = -6 Total displacement is 6 units due South. Note that there was only displacement in one direction, so we could just use final - initial to easily calculate displacement. If there was displacement in multiple directions we would have to do something else, which is to use the distance formula

A ball is dropped off of a skyscraper. When it hits the ground, it is clocked as travelling at 467 m/s. How long was the ball falling from the top skyscraper?

(A) 47.65 s Acceleration = Change in Velocity / Change in Time 9.8 (gravity) = 467 / Change in Time Change in Time = 467 / 9.8 Change in Time = approx. 47 seconds (actual: 47.65) Note this is assuming a constant acceleration Change in velocity is (final- initial)

What would the area underneath a Velocity vs Time graph represent?

(A) Displacement

Which of the following statements about Terminal Velocity are true? I. Terminal Velocity can differ for the same free-falling object, depending on the medium it falls through. II. Terminal Velocity is characterized by oscillating accelerations, leading to a constant velocity. III. Terminal Velocity is only possible on Earth.

(A) I only Each of the following statements about terminal velocity are true: I. Terminal Velocity can differ for the same free-falling object, depending on the medium it falls through. II. Terminal Velocity is characterized by the forces of gravity and resistance through the medium being traveled through being equal and opposite, leading to a constant velocity.

Johnny was running away from some bullies at school. His friend was running with him and wanted to help him run faster, so he started pushing him forward with a force of 11.23 Newtons. If Johnny has a mass of 48.9 kg, what was Johnny's acceleration?

(B) 0.230 m/s^2 Force/mass = acceleration 11.23/48.9 = acceleration acceleration = approx. 0.2 m/s^2 (actual: .23)

If Max got in his car and traveled northwest, with a 63.2° angle between his direction and due west, how far west (in miles) would he have gone if he went 26.6 miles in the northwest direction? (A) 4.6 (B) 12.0 (C) 16.8 (D) 34.2

(B) 12.0 cosθ = adjacent/hypotenuse cos63.2 = adjacent/26.6 adjacent = (26.6)(cos63.2) adjacent = (26.6)(approx. .5 (actual: .451)) adjacent = (approx. 13.3 (actual: .12.0))

Joshua drove 17.45 miles in 23.4 minutes. His total displacement, however, was only 9.44 miles in the north direction. What was his average velocity (in mph)?

(B) 24.2 Average velocity = displacement/change in time Average Velocity = (9.44 miles) / (23.4/60 hour) Average Velocity = (9.44 miles) / (approx. 1/3 hour) Average Velocity = approx. 30 mph (actual: 24.2)

In which of the following examples could you calculate the missing variable from given information? I. Given Distance and Initial Position, find Final Position. II. Given Initial Position and Distance, find Final Position. III. Given Initial Position and Final Position, Find Displacement. (A) I only (B) III only (C) I and II only (D) I, II and III

(B) III only If you know the Initial and Final position, you can find Displacement. However, knowing distance cannot help to find Initial or Final Positions, since distance has no direction, only magnitude!

Johnny got tired of running so fast (3 m/s), so he started slowing down at a rate of (0.2 m/s^2). What was his final velocity after 7 seconds of this deceleration?

(C) 1.6 (Final Velocity) = (Initial Velocity) + ((Time)x(Acceleration)) Final Velocity = (3 m/s) + ((-0.2 m/s^2)(7 s)) Final Velocity = 1.6 m/s Note that "slowing down" means the acceleration will have the opposite sign compared to the initial velocity. Also looking at it conceptually: For every second, Johnny's speed will slow down by 0.2 m/s

What would the slope of a Velocity vs Time graph represent?

(C) Acceleration

Sally is pushing a box along the floor to the right with a constant velocity of 4.23 m/s. Which of the following is true? I. Sally is exerting a force on the box. II. The box is experiencing a net force of zero. III. The box is falling with a constant acceleration.

(C) I and II Only I. Sally is exerting a force on the box. This is true! We have to know tho that there was to be a force the box is also be affected by in the opposite direction that gives this a Fnet of 0 which is why there is no acceleration and a constant velocity II. The box is experiencing a net force of zero. This is also true because the frictional force is equal to the force exerting by Sally; thus, the box is moving at a CONSTANT velocity and is not accelerating. III. The box is falling with a constant acceleration. This is false because gravity is opposed by the equal and opposite normal force.

Ali is running at 1.22 m/s in the positive direction. Over 19.44 seconds he increases his speed to 2.31 m/s, what is his average acceleration?

(D) 0.056 m/s^2 Acceleration = change in velocity / change in time Acceleration = ( 2.31 - 1.22 m/s) / (19.44 s) Acceleration = 0.05 m/s^2 (actual: .056 m/s^2)

What is the equation for final velocity in terms of initial velocity and acceleration?

(Final Velocity) = (Initial Velocity) + ((Time)x(Acceleration))

What is a cross product?

A cross product is the product of the magnitude of two vectors and the sin of the angle between them. Note that if you are given an x component and y component as vectors then the angel between them is 90 degrees

What is a scalar?

A quantity with a magnitude only

What is a vector

A quantity with a number and a direction

What is force?

An action that is capable of causing acceleration

What is Newton's First Law?

An object at rest or in motion with constant velocity will remain that way unless a force acts on it. Note that something with a constant velocity or a velocity of 0 will have an acceleration of 0 , thus no force is being applied to it

What is Netwon's Second Law?

An object of mass m will accelerate when the vector sum of the forces (Fnet) results in some nonzero resultant force vector. No acceleration will occur when the vector sum of the forces results in a cancellation of those forces

How is average velocity calculated from displacement?

Average velocity = displacement/change in time

Johnny was traveling at a speed of 14.2 m/s and traveled a total of 345.9 meters. How long did it take?

B) 24.36 s Average velocity = displacement/change in time 14.2 = 345.9 / change in time change in time = 345.9 / 14.2 change in time = approx. 23 seconds (actual: 24.36)

If Newton's first law states that something will be constantly moving at a certain velocity, how comes thing eventually stop after we initially push them?

Because the unbalanced force in the opposite direction that is acting on it in the process is friction and overtime it will stop. The force of friction overcomes the applied force. And also air resistance helps to slow it down

If we know the angle of a vector and adjacent horizontal vector, how can we use that to find the length of the original vector (the hypotenuse)?

By using cosθ = adjacent/hypotenuse

What does multiplying a vector by a negative number do?

Change the magnitude and direction of the vector.

How does one break a vector into components?

Choose two axes (vertical & horizontal or parallel & perpendicular) and use two vectors to represent the original vector.

When multiplying vectors, what type of product should be used to create a new vector?

Cross Product

If Johnny starts his car and floors it, he accelerates constantly until he reaches a velocity of 62.44 m/s, which takes about 46.7 seconds. How far does he travel in that time?

D) 1458 Average velocity = (62.44 m/s + 0 m/s)/ 2 = approx. 30 m/s (actual 31.22 m/s) This can only be done under the assumption of a constant acceleration (Average Velocity) x (Time) = Displacement ((62.44 + 0)/ 2) x (46.7) = Displacement (31.22)(46.7) = Displacement Displacement = approx. 1500 (actual: 1457.97)

What does the area under the curve represent in a velocity vs. time graph?

Displacement

What is the equation for displacement in terms of average velocity? ex. In KHAN video we wanted to find out how much distance is needed for the plane to take off after finding time it takes using velocity and acceleration

Displacement = (Average Velocity) x (Time) This comes from the equation defining average velocity, shown in the image. Note if acceleration is constant which we can most of the time assume, then average velocity is final + initial all divided by two

How do you calculate displacement?

Displacement = Final Position - Initial Position = Net Distance (in some direction) Shortest distance between two points

What is displacement?

Displacement is a vector quantity that describes an objects change in position in space. It is an arrow from initial position to final position.

What is distance?

Distance is a scalar quantity that describes the length that an object has traveled. It is a tallying of the total length an object has moved to get from its initial position to its final position.

When multiplying vectors, what type of product should be used to create a scalar?

Dot product

True or False? Speed will always be changed by an unbalanced force acting on the object.

False. An unbalanced force can change the direction of an object without changing the speed. The sentence should say, "VELOCITY will always be changed by an unbalanced force acting on the object." Because velocity has to do with direction as well and not just magnitude like speed. Magnitude often times will change but it doesn't have to

If an object's velocity is zero, then the object's acceleration must also be zero. If false, provide a counterexample.

False. Even if an object's velocity is zero, the object could still be accelerating. Think of a baseball thrown straight up into the air; there is a split second where the ball is not moving up or down (at it peak height), but gravity is still making the ball accelerate back towards the Earth.

Recall the prompt: Benny "The Jet" hit a baseball so hard one day that it broke a window. Benny was shocked that the ball and glass both went inside the building, thinking that the equal forces in opposite directions should have made one land inside the building and the other land outside. True or false? The baseball still traveling in a direction opposing the net force acting upon the baseball can be attributed to inertia.

False. Inertia would apply if there had been no net force acting on the baseball at all. There clearly is a force exerted on the baseball by the window, as stated in the question stem.

True of False? An unbalanced force on an object will always change objects direction

False. Just like you wont always change an objects speed, you wont always change on objects direction because you could apply an unbalanced force going in the same direction the object is already going

True or false? Newton's First Law could be seen as a special case of Newton's Third law, where the reaction is equal to zero.

False. Newton's First Law could be seen as a special case of Newton's Second law, where the acceleration is equal to zero.

Recall the prompt: A ball is dropped off of a skyscraper. When it hits the ground, it is clocked as travelling at 467 m/s. True or false? Terminal Velocity was reached right before the ball hit the ground, since the ball after that moment started decelerating.

False. Terminal Velocity was clearly not reached right before the ball hit the ground, since the ball was still accelerating right before it hit the ground. Recall that terminal velocity is the point at which the force of the air resistance is equal to the weight of the object (m*g) giving a net force of zero, and the object will no longer be accelerating, instead it will be at a constant velocity

True or false? Air Resistance is the sole type of Drag Force seen in nature. If false, provide a counterexample.

False. There are many types of resistance that can result in Drag Force. For a counterexample, Drag Forces can be seen in the circulatory system due to viscous friction of the blood!

Which component of a vector will cos(theta) give you? (horizontal/vertical and parallel/perpendicular)

Horizontal or Perpendicular

Match the following xyz-plane directions with their corresponding unit vectors. I. x II. y III. z (A)h^ (B)î (C)ĵ (D)k^

I (B) x: î II (C) y: ĵ III (D) z: k^

We know that the equations given for average velocity, speed, etc, are just averages overtime as the unit of measure probably changes over the course of time (meaning the instantaneous measurements may have been different along the path). How can we calculate instantaneous measurement (using velocity ass an example)?

If the avg velocity is constant over the distance for that certain time frame then avg velocity = instantaneous velocity If velocity is changing then you can use a displacement vs time graph and the slope of the tangent line at a certain time point is the instantaneous velocity If acceleration is constant, the you can use the kinematic formula to find the instantaneous velocity at any time t. This formula is v= vi+at

Newton's First Law is often referred to as the Law of Inertia. Define Inertia.

Inertia can best be described as a tendency to remain unchanged, whether that is moving uniformly straight or being at rest.

What is the difference between instantaneous speed and instantaneous velocity?

It includes direction unlike instantaneous speed. Notice how both the magnitude and direction are highlighted

What does "instantaneous" mean when referring to velocity (or speed of acceleration, etc)?

It means the velocity, speed, acceleration,etc, at a specific time, not an average over a period of time. Notice for speed how only the magnitude is highlighted

Newton's first law is also known as:

Law of Inertia

What are the units for force?

Newtons or ((kg*m)/s^2)

Two students, Ryan and Akeem, were fighting over if an object can have forces acting on it and not accelerate. Ryan argued that forces are directly related to acceleration, so any object with a force or forces acting on it must be accelerating in some direction. Is Ryan correct? If not, provide a counterexample.

Ryan is not correct, because he is forgetting about vector addition and the possibility of opposing forces. If the vectors for each force add up to 0 magnitude, then there will be no "net force", and there will be no acceleration.

What does soh cah toa stand for?

Sinθ = opposite/hypotenuse Cosθ = adjacent/hypotenuse Tanθ = opposite/adjacent

What is speed?

Speed is a scalar quantity that tallies the length of distance travelled over time.

How does one approach a projectile motion problem?

Split all motion into x and y components.

How does one calculate the magnitude of a vector from its components?

Square both component vector magnitudes, add them, and square root the sum. Note that if angles are present then soh cah toa can be used

How does one calculate the average velocity of an object?

Take the change in (displacement) and divide it by the change in time.

How do the components of vectors add when two overall vectors are summed?

The components themselves simply sum.

What is air resistance?

The force of friction with the air. This force opposes movement and increases as speed increases, and eventually this drag force will be equal in magnitude to the weight (m*g) - (recall that weight is a force) of the object and the object will fall with constant velocity according to new tons first law. This velocity is called the terminal velocity where the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.

What does the slope at a point on a position vs time graph represent?

The instantaneous velocity at that point.

What is a dot product?

The product of the magnitudes of two vectors and the cosine of the angle between them. Note that if you are given an x component and y component as vectors then the angel between them is 90 degrees

Describe the tail to tip method?

The tail to tip method is a way of calculating the sums (or subtractions) of vectors. Simply put the vectors tail to tip (flip the vector for negative) Note that the sum of the two vectors must be greater or equal to the difference of their magnitudes, but smaller or equal to the sum of their magnitudes. So note that if A is 3 and B is 5, that does not necessarily mean that C is 8

Instantaneous velocity and instantaneous speed are equivalent. Why?

This makes sense because it takes time to change the direction of a vector. In velocity, you're moving at some speed and you can change direction at some point. In speed, you're just moving at some speed not worrying about direction. In any given instant, you are only travelling in one direction. It takes time to turn and go into different directions, messing with displacement and therefore velocity. Therefore, with a timescale of 0 (instantaneous) velocity is only going in one direction and is therefore equivalent to instantaneous speed.

Benny "The Jet" hit a baseball so hard one day that it broke a window. Benny was shocked that the ball and glass both went inside the building, thinking that the equal forces in opposite directions should have made one land inside the building and the other land outside. Where did Benny go wrong in this logic?

Those equal forces in opposite directions do occur! That force of the outside baseball striking the window provides a force towards the inside of the building, explaining the glass. The glass also exerts the same force going away from the building on the baseball; however, that baseball was traveling at a high velocity, and that force only decelerates the ball, not change the direction of its velocity entirely.

Which variable links the horizontal and vertical aspects of projectile motion?

Time. Once the ball hits the ground, the motion stops, both horizontal and vertical. Therefore, time is the one variable that you can solve for in one dimension and then use in another. This fact will often provide the necessary variables for solving certain kinematics problems.

What is the purpose of the right hand rule?

To determine the direction of the resultant vector of a cross product.

What is Newton's Third Law?

To every action(force), there is always an opposed but equal reaction. Law states that for every force exerted by object A on object B, there is an equal but opposite force exerted by object B on object A.

True or False? An object at rest will never move until it is acted on by an unbalanced Force.

True. An object at rest will never move until it is acted on by an unbalanced Force.

True or False? An object being acted on by an unbalanced Force in a specific direction will accelerate in that direction

True. An object being acted on by an unbalanced Force will accelerate.

True or false? An object's average acceleration must be in the same direction as the object's change in velocity. If false, provide a counterexample.

True. An object's average acceleration must be in the same direction as the object's change in velocity.

True or false? Displacement, unlike Distance, can be used when knowing one of Final or Initial to find the other because Displacement has both a magnitude and a direction.

True. Displacement, unlike Distance, can be used when knowing one of Final or Initial to find the other because Displacement has both a magnitude and a direction.

True or false? If there is a non-zero net force, there must be acceleration.

True. If there is a non-zero NET force, there must be acceleration.

True or false? Inertia dictates the velocity of an object if the acceleration of that object is zero.

True. Inertia dictates the velocity of an object if the acceleration of that object is zero.

True or false? When multiplying a vector by a positive (n>0) number, the magnitude of the vector will change, but not its direction.

True. When multiplying a vector by a positive (n>0) number, the magnitude of the vector will change, but not its direction.

What are unit vectors and what is the purpose?

Unit vectors are vectors with a magnitude of one and the way they are used is that we can define the x,y,or z component of a vector as a multiple of the specific unit vector that correlates to that plane. The importance of this is that it helps us to analytically express any two dimensional vector instead of having to draw out its component parts as we did before. WE can add or subtract without having to resort to visual means

What does vector b̂ = 4î + 3ĵ mean?

Vector b can be broken down into a horizontal vector of length 4 and a vertical vector of length 3.

What is the difference between a vector and a scalar?

Vectors have magnitude (size) AND direction. Scalars just have magnitude (size).Ex. An object moved 5m is a scalar wheras an object moved 5m to the right is a vector

What is velocity?

Velocity is a vector quantity that describes the change in displacement per unit of time.

What is the difference between velocity and speed?

Velocity is a vector quantity, while speed is a scalar quantity. Speed = absolute value of velocity if they have the same magnitude (aka if displacement has same magnitude as distance under the same time)

What is the difference in units for velocity and acceleration?

Velocity= m/s Acceleration= m/s^2

Which component of a vector will sin(theta) give you? (horizontal/vertical and parallel/perpendicular)

Vertical or Parallel

What would a negative value for acceleration represent?

deceleration or slowing down

The acceleration of an object is ___________ proportional to net force and ____________ proportional to its mass

directly and inversely

A person starts off at 0 and moves 10 m to the right and then 5 m to the left, what is distance vs displacement?

distance: 15m displacement : 5 m Note distance is total area traveled and displacement is final position- initial position Also note, if the person came back to the left 10 m then displacement would've been 0

Scalar is to ____________ as vector is to___________.

distance; displacement Displacement includes a direction and a quantity; therefore, it is a vector quantity. Distance, on the other hand, is a scalar quantity as it only entails a quantity.

How does one use the right hand rule?

for C = A x B 1. Point thumb in the direction of vector A 2. Point fingers in the direction of vector B 3. The direction your palm is facing is the direction of vector C

What is linear motion?

motion in a straight line. However it is not limited to horizontal or vertical paths.

What is projectile motion?

motion that follows a path along two dimensions. So the velocities and accelerations in the two directions are independent of each other and must accordingly be analyzed separately