Understanding Distances - AP Physics C: Electricity and Magnetism
Card 1 of 55
An object starts from rest and reaches a velocity of 
after accelerating at a constant rate for four seconds. What is the distance traveled in this time?
An object starts from rest and reaches a velocity of
Tap to reveal answer
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
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At the moment a car is passed by another car constantly traveling at 
, it begins to accelerate at 
. In how many seconds does this car catch up to and pass the other car?
At the moment a car is passed by another car constantly traveling at
Tap to reveal answer
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for 
.
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
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An object moving along a line has a displacement equation of 
, where 
is in seconds. For what value of 
is the object stationary?
An object moving along a line has a displacement equation of
Tap to reveal answer
Use the fact that 
to find the velocity equation, and then solve for 
when 
.
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
Use the fact that
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
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An object is moving on a line and has displacement equation of 
, where 
is in seconds. At what value of 
is the object not accelerating?
An object is moving on a line and has displacement equation of
Tap to reveal answer
Take the second derivative of 
, to find the acceleration function 
. Then find the value of 
where 
. The fact that it is simply 
and not 
or 
inside that quantity means that using the Chain Rule becomes decidedly easier.
Set the acceleration fuction equal to zero and solve for the time.
Take the second derivative of
Set the acceleration fuction equal to zero and solve for the time.
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A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
Tap to reveal answer
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
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An object starts from rest and reaches a velocity of after accelerating at a constant rate for four seconds. What is the distance traveled in this time?
An object starts from rest and reaches a velocity of
Tap to reveal answer
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
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At the moment a car is passed by another car constantly traveling at , it begins to accelerate at . In how many seconds does this car catch up to and pass the other car?
At the moment a car is passed by another car constantly traveling at
Tap to reveal answer
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for .
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
← Didn't Know|Knew It →
An object moving along a line has a displacement equation of , where is in seconds. For what value of is the object stationary?
An object moving along a line has a displacement equation of
Tap to reveal answer
Use the fact that to find the velocity equation, and then solve for when .
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
Use the fact that
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
← Didn't Know|Knew It →
An object is moving on a line and has displacement equation of , where is in seconds. At what value of is the object not accelerating?
An object is moving on a line and has displacement equation of
Tap to reveal answer
Take the second derivative of , to find the acceleration function . Then find the value of where . The fact that it is simply and not or inside that quantity means that using the Chain Rule becomes decidedly easier.
Set the acceleration fuction equal to zero and solve for the time.
Take the second derivative of
Set the acceleration fuction equal to zero and solve for the time.
← Didn't Know|Knew It →
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
Tap to reveal answer
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
← Didn't Know|Knew It →
An object starts from rest and reaches a velocity of after accelerating at a constant rate for four seconds. What is the distance traveled in this time?
An object starts from rest and reaches a velocity of
Tap to reveal answer
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
← Didn't Know|Knew It →
At the moment a car is passed by another car constantly traveling at , it begins to accelerate at . In how many seconds does this car catch up to and pass the other car?
At the moment a car is passed by another car constantly traveling at
Tap to reveal answer
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for .
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
← Didn't Know|Knew It →
An object moving along a line has a displacement equation of , where is in seconds. For what value of is the object stationary?
An object moving along a line has a displacement equation of
Tap to reveal answer
Use the fact that to find the velocity equation, and then solve for when .
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
Use the fact that
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
← Didn't Know|Knew It →
An object is moving on a line and has displacement equation of , where is in seconds. At what value of is the object not accelerating?
An object is moving on a line and has displacement equation of
Tap to reveal answer
Take the second derivative of , to find the acceleration function . Then find the value of where . The fact that it is simply and not or inside that quantity means that using the Chain Rule becomes decidedly easier.
Set the acceleration fuction equal to zero and solve for the time.
Take the second derivative of
Set the acceleration fuction equal to zero and solve for the time.
← Didn't Know|Knew It →
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
Tap to reveal answer
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
← Didn't Know|Knew It →
An object starts from rest and reaches a velocity of after accelerating at a constant rate for four seconds. What is the distance traveled in this time?
An object starts from rest and reaches a velocity of
Tap to reveal answer
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
Since the acceleration is constant in this problem, we can apply the kinematics given equation to calculate the distance:
First, we need to calculate the acceleration.
Plug in our velocity and time values to find the acceleration.
Now we can return to the kinematics equation and solve for the distance traveled:
← Didn't Know|Knew It →
At the moment a car is passed by another car constantly traveling at , it begins to accelerate at . In how many seconds does this car catch up to and pass the other car?
At the moment a car is passed by another car constantly traveling at
Tap to reveal answer
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for .
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
First, find the displacement equations for both cars. Car 1 will be the car that is initially stationary; car 2 will be the car traveling with constant velocity.
Car 1:
Car 2:
Now, set those displacement equations equal to each other and solve for
The accelerating car will catch and pass the car traveling at constant velocity after 4 seconds.
← Didn't Know|Knew It →
An object moving along a line has a displacement equation of , where is in seconds. For what value of is the object stationary?
An object moving along a line has a displacement equation of
Tap to reveal answer
Use the fact that to find the velocity equation, and then solve for when .
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
Use the fact that
Take the derivative of the displacement equation.
Set the velocity equal to zero.
Solve for the time.
← Didn't Know|Knew It →
An object is moving on a line and has displacement equation of , where is in seconds. At what value of is the object not accelerating?
An object is moving on a line and has displacement equation of
Tap to reveal answer
Take the second derivative of , to find the acceleration function . Then find the value of where . The fact that it is simply and not or inside that quantity means that using the Chain Rule becomes decidedly easier.
Set the acceleration fuction equal to zero and solve for the time.
Take the second derivative of
Set the acceleration fuction equal to zero and solve for the time.
← Didn't Know|Knew It →
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
A projectile is launched out of a cannon or launch tube with zero air resistance or friction. At what angle (in degrees) should the projectile be launched to maximize the distance it travels?
Tap to reveal answer
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
The projectile travels the farthest when the vertical component of its velocity matches the sum of its horizontal component and whatever the wind/friction adds or subtracts. If the wind has no effect, then a 45-degree angle will be the best because the horizontal and vertical components of the velocity will create a right isosceles triangle (remember special triangles).
← Didn't Know|Knew It →