Understanding Distance, Velocity, and Acceleration - High School Physics
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Leslie rolls a ball out of a window from 10 meters above the ground, such that the initial y-velocity is zero. How long will it be before the ball hits the ground?
Leslie rolls a ball out of a window from 10 meters above the ground, such that the initial y-velocity is zero. How long will it be before the ball hits the ground?
We are given the initial velocity, acceleration, and distance traveled. Using the equation below, we can solve for the time.
The distance is negative, which makes since because the ball is traveling downward.
We are given the initial velocity, acceleration, and distance traveled. Using the equation below, we can solve for the time.
The distance is negative, which makes since because the ball is traveling downward.
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Derek rolls a ball along a flat surface with an initial velocity of 
. If it stops after 12 seconds, what was the acceleration on the ball?
Derek rolls a ball along a flat surface with an initial velocity of
Since the ball starts with a positive velocity and ends at rest, we can predict that the acceleration will be negative. Using the values given in the question and the equation below, we can solve for the acceleration.
Since the ball starts with a positive velocity and ends at rest, we can predict that the acceleration will be negative. Using the values given in the question and the equation below, we can solve for the acceleration.
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Derek rolls a ball along a flat surface with an initial velocity of 
. If it stops after 12 seconds, what was the total distance it travelled?
Derek rolls a ball along a flat surface with an initial velocity of
We can solve this question by multiplying the average velocity by the time.
We are given the initial and final velocities and the time travelled.
We can solve this question by multiplying the average velocity by the time.
We are given the initial and final velocities and the time travelled.
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Peter starts from rest and runs down a hallway 31 seconds. If his final velocity is 
, how far did he run?
Peter starts from rest and runs down a hallway 31 seconds. If his final velocity is
Using the given values for the initial velocity, final velocity, and time, we can solve for the distance. The distance will be the product of the average velocity and the time.
Using the given values for the initial velocity, final velocity, and time, we can solve for the distance. The distance will be the product of the average velocity and the time.
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Walter throws a disc from 1.5 meters above the ground with purely horizontal motion. If he throws it with an initial velocity of 
and it stays in the air for 0.553 second, how far will it travel?
Walter throws a disc from 1.5 meters above the ground with purely horizontal motion. If he throws it with an initial velocity of
The horizontal velocity will determine how far the disc travels; gravity and vertical velocity will not affect the horizontal distance. We can solve by using the distance formula.
The horizontal velocity will determine how far the disc travels; gravity and vertical velocity will not affect the horizontal distance. We can solve by using the distance formula.
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Laurence throws a 
rock off the edge of a 
tall building at an angle of 
from the horizontal with an initial speed of 
.
.
A 
rock is thrown with the same initial velocity and angle from the top of the building. How would the horizontal distance traveled by this rock compare to the horizontal distance traveled by the lighter rock?
Laurence throws a
A
The equation for distance travelled in the horizontal direction is:
There is no acceleration in the horizontal direction, so this velocity is constant throughout flight.
There is no place for mass in this equation. Any objects thrown with the same velocity will travel the same distance. The two rocks with thus travel the same horizontal distance.
The equation for distance travelled in the horizontal direction is:
There is no acceleration in the horizontal direction, so this velocity is constant throughout flight.
There is no place for mass in this equation. Any objects thrown with the same velocity will travel the same distance. The two rocks with thus travel the same horizontal distance.
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Sam throws a 
rock off the edge of a 
tall building at an angle of 
from the horizontal. The rock has an initial speed of 
.
If Sam then threw a 
rock instead, how would this affect its total horizontal distance travelled?
Sam throws a
If Sam then threw a
The equation for distance travelled in the x-direction with parabolic motion is 
.
The mass of the object is not a variable in this calculation, and will not alter the horizontal velocity.
This can also be observed by analyzing the units for the velocity calculation.
Kilograms are not involved in the units, so mass will not be involved.
Changing the mass will not change the distance travelled; the rock will travel the same distance.
The equation for distance travelled in the x-direction with parabolic motion is
The mass of the object is not a variable in this calculation, and will not alter the horizontal velocity.
This can also be observed by analyzing the units for the velocity calculation.
Kilograms are not involved in the units, so mass will not be involved.
Changing the mass will not change the distance travelled; the rock will travel the same distance.
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Julia throws a 
rock at 
above the horizontal, with an initial velocity of 
.
If she were throwing a 
rock instead, how would this affect the total horizontal displacement?
Julia throws a
If she were throwing a
The equation for horizontal distance travelled during parabolic (projectile) motion is:
The distance is related to the velocity and the flight time only. The mass of the projectile will not affect any of these variables, and therefore will not affect the distance travelled.
We can also analyze this formula in terms of the units and dimensional analysis.
There is no units for mass or 
anywhere in the calculation, so mass will not be involved in determining the final answer.
A change in the mass will not change the distance travelled; the projectile will travel the same distance.
The equation for horizontal distance travelled during parabolic (projectile) motion is:
The distance is related to the velocity and the flight time only. The mass of the projectile will not affect any of these variables, and therefore will not affect the distance travelled.
We can also analyze this formula in terms of the units and dimensional analysis.
There is no units for mass or
A change in the mass will not change the distance travelled; the projectile will travel the same distance.
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A 
box starts at rest and reaches a velocity of 
after traveling a distance of 
. What was the acceleration on the box?
A
The best formula for this will be 
.
We are given the initial velocity (zero because the box starts at rest), final velocity, and distance. Using these values, we can solve for the acceleration. We are also given the mass, but this is extraneous information.
Divide both sides by 
.
The best formula for this will be
We are given the initial velocity (zero because the box starts at rest), final velocity, and distance. Using these values, we can solve for the acceleration. We are also given the mass, but this is extraneous information.
Divide both sides by
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A crate slides across a floor. After 
it has a velocity of 
. After 
it has a velocity of 
. What is the acceleration?
A crate slides across a floor. After
Acceleration is the change in velocity over the change in time:
In this case, even though we look at the crate after different times, the velocity hasn't changed at all.
If there is no change in the velocity, then the acceleration must be equal to zero.
Acceleration is the change in velocity over the change in time:
In this case, even though we look at the crate after different times, the velocity hasn't changed at all.
If there is no change in the velocity, then the acceleration must be equal to zero.
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An object starts sliding along a floor at a speed of 
. After 
, it is observered that the object is sliding with a speed of 
. What is the average acceleration of the object?
An object starts sliding along a floor at a speed of
Notice that at the beginning and at the end of the problem, the velocity of the object is 
. Acceleration is 
. Since there is no change in velocity, acceleration is calculated as 
, so the acceleration is 
.
Notice that at the beginning and at the end of the problem, the velocity of the object is
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During a storm, you can usually see the lightning before you hear the thunder, unless you are very close to the lightning strike. What causes this discrepancy?
During a storm, you can usually see the lightning before you hear the thunder, unless you are very close to the lightning strike. What causes this discrepancy?
Assuming you stand in one place, the distance between you and the lightning strike does not change.
The formula for velocity is:
In this scenario, the distance travelled, 
, does not change. The time taken to travel this distance, 
, does change. That means that the velocity must also be changing.
This is an indirect relationship. As 
increases, 
will decrease; thus, the object with a greater time of travel (sound) will have a slower velocity.
Assuming you stand in one place, the distance between you and the lightning strike does not change.
The formula for velocity is:
In this scenario, the distance travelled,
This is an indirect relationship. As
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A mass moves a constant velocity, 
, for a certain amount of time, 
. How far does it travel?
A mass moves a constant velocity,
The relationship between velocity, distance, and time is:
We can multiply both sides by 
to see solve for the distance traveled, in terms of the time and velocity.
The product of time and velocity, 
, will give us the distance we are looking for.
The relationship between velocity, distance, and time is:
We can multiply both sides by
The product of time and velocity,
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An object starts at rest and reaches a velocity of 
after 
seconds. What is the average acceleration of the object?
An object starts at rest and reaches a velocity of
The relationship between acceleration and velocity is:
Acceleration is equal to the change in velocity over the change in time. If the object starts from rest, then we can set up an equation to solve for the change in velocity.
Using the terms from the question, we can see that the acceleration will be equal to the final velocity divided by the time.
The relationship between acceleration and velocity is:
Acceleration is equal to the change in velocity over the change in time. If the object starts from rest, then we can set up an equation to solve for the change in velocity.
Using the terms from the question, we can see that the acceleration will be equal to the final velocity divided by the time.
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A balls starts at rest, then begins to move with a negative acceleration. Describe the motion of the ball.
A balls starts at rest, then begins to move with a negative acceleration. Describe the motion of the ball.
Acceleration is a vector. This means that positive and negative signs are used to help us understand the direction of motion. If something has a negative acceleration it CAN mean that it is slowing down, but not always. Negative usually means that an object is moving to the left, down, or backwards. If the ball begins from rest, and has a negative acceleration, then it is gaining a negative velocity. This simply refers to a velocity in a negative, or backwards, direction.
Acceleration is a vector. This means that positive and negative signs are used to help us understand the direction of motion. If something has a negative acceleration it CAN mean that it is slowing down, but not always. Negative usually means that an object is moving to the left, down, or backwards. If the ball begins from rest, and has a negative acceleration, then it is gaining a negative velocity. This simply refers to a velocity in a negative, or backwards, direction.
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A boy jogs down a 
street in 
. What was his average velocity?
A boy jogs down a
Velocity is change in displacement over change in time.
We are given the distance traveled and the time period. Using these values, we can find the velocity.
Velocity is change in displacement over change in time.
We are given the distance traveled and the time period. Using these values, we can find the velocity.
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Which of these is the correct relationship between velocity, distance, and time?
Which of these is the correct relationship between velocity, distance, and time?
Velocity is defined by a change in distance during a period of time. It is a rate of movement.
The magnitude of velocity is equal to the quotient of the change in distance and the change in time.
Velocity is defined by a change in distance during a period of time. It is a rate of movement.
The magnitude of velocity is equal to the quotient of the change in distance and the change in time.
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A ball begins to roll with a velocity 
. If there is no acceleration on the ball, what will its velocity be after 
?
A ball begins to roll with a velocity
If there is no acceleration on an object, it will have the same velocity regardless of how long it is moving.
Mathematically, we can look at the equation for acceleration.
We know that the acceleration is zero and that the time is ten seconds.
In order for this to be true, the initial and final velocities must be equal.
If there is no acceleration on an object, it will have the same velocity regardless of how long it is moving.
Mathematically, we can look at the equation for acceleration.
We know that the acceleration is zero and that the time is ten seconds.
In order for this to be true, the initial and final velocities must be equal.
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A plane originally travelling north at 
is informed that a storm is moving into its intended path at a rate of 
every forty minutes. By how much must the plane increase its velocity in order to outpace the storm?
A plane originally travelling north at
Our first step is to calculate the velocity of the storm in the proper units.
In order for the plane to move faster than the storm, its velocity must be greater than this value. To find the necessary increase in velocity, we need to subtract the initial velocity from the final velocity.
This is the necessary increase in velocity in order for the plane to match the pace of the storm; thus, our answer must be only slightly greater than 
. This leads to our answer of 
.
Our first step is to calculate the velocity of the storm in the proper units.
In order for the plane to move faster than the storm, its velocity must be greater than this value. To find the necessary increase in velocity, we need to subtract the initial velocity from the final velocity.
This is the necessary increase in velocity in order for the plane to match the pace of the storm; thus, our answer must be only slightly greater than
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An athlete kicks a ball into the air. It travels 
and is in the air for 
. How fast must the athlete run from the point where he kicks the ball in order to catch it before it lands?
An athlete kicks a ball into the air. It travels
To solve this problem, we need to understand what speed is. Speed is the distance covered in a given amount of time.
In our problem, we need to find the speed of the athlete. We are given the distance the athlete must cover, which is equal to the distance traveled by the ball.
We are also told how much time the athlete has to cover the distance, which is equal to the time the ball is in the air.
Use these values and the equation for speed to find the speed that the athlete must run.
To solve this problem, we need to understand what speed is. Speed is the distance covered in a given amount of time.
In our problem, we need to find the speed of the athlete. We are given the distance the athlete must cover, which is equal to the distance traveled by the ball.
We are also told how much time the athlete has to cover the distance, which is equal to the time the ball is in the air.
Use these values and the equation for speed to find the speed that the athlete must run.
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