All AP Physics 1 Resources
Example Questions
Example Question #74 : Motion In One Dimension
Sally () runs at to try out her new, stationary, hoverboard . What will be her resulting velocity on the hoverboard (if she is able to maintain her balance)?
This is a conservation of momentum problem:
where the subscripts refer to , and
Now, let's plug in the relevant information. Remember, the hoverboard is initially stationary, so its velocity is zero. Also, for the final mass, we need to add the two masses, since now Sally is on top of the hoverboard.
Now, all we need to do is solve for the final velocity:
Example Question #75 : Motion In One Dimension
How long will it take a person to travel a distance of if they are starting from rest and accelerating at a constant rate of ?
For this question, we're told that a runner begins at rest and travels a certain distance with a constant acceleration. We're asked to determine how much time it takes for this to happen.
Right off the bat, it's important to realize that we can use the kinematics equations because we are told that the acceleration is constant. Now, we need to use an equation that relates distance, time, and acceleration.
Since we know that the person is starting from rest, their initial velocity must be zero. Thus, we can simplify the above expression.
Now, we can go ahead and rearrange this expression to isolate the variable for time.
Lastly, we just need to plug in the values given to us in the question stem in order to solve for our answer.
Example Question #72 : Linear Motion And Momentum
Suppose that two objects, both of equal mass, are traveling in the same direction but at different velocities. At a certain point, one of the objects collides with the other one and, from then on, both objects travel together as one. Which of the following expressions gives the momentum as both objects travel together?
In this question, we're told that two objects of equal mass eventually collide with each other and then travel together. We're asked to find an expression that tells us the final momentum of the system.
First, we can recognize this as an inelastic collision, which means that momentum is conserved in our system of the two objects but kinetic energy is not. Also, because both objects travel together after the collision, there will be a single final velocity.
Thus, the final momentum of our system of two objects can be expressed as .
Example Question #72 : Motion In One Dimension
A ball is thrown straight up in the air with an initial velocity of .
What is the ball's velocity at its maximum height?
At a projectiles maximum height its y-direction velocity is always . It is moving neither up nor down. Because the ball was thrown straight in the air, there is no x-direction component of its velocity to account for.
Example Question #74 : Linear Motion And Momentum
A ball is thrown straight up in the air with an initial velocity of .
What is the ball's acceleration at its maximum height? The acceleration due to gravity can estimated at .
Gravity is the only force acting on the ball at its maximum height. Though the ball has zero velocity at this point, gravity is still accelerating the ball at . Gravity almost always pulls down, which is a negative direction in the traditional coordinate system so our answer must be negative.
Example Question #73 : Motion In One Dimension
A baseball pitcher throws a fastball at a speed of . If the average reaction time of a professional baseball player is , how far has the ball traveled by the time the batter reacts?
We can calculate the distance traveled by multiplying the velocity of the ball by the reaction time of the batter. However, we will need to first need to get the appropriate units:
Now we can simply multiply this by the reaction time of the batter to get the distance that the ball has traveled by the time her reacts:
Fun fact: the distance from the pitching mound to home plate is about , so the ball is about halfway to the plate by the time the batter begins to react.
Example Question #81 : Motion In One Dimension
A baseball batter hits a ball straight up in the air at a velocity of . If the ball hits the bat at a height of above the ground, how long does it take for the ball to hit the ground?
There air multiple ways to solve this problem, so don't worry if you attacked this problem from a different angle. This following method avoids using the quadratic formula:
First, we will calculate how long it takes for the ball to travel upward, and then come back down to its original height.
Since we are neglecting air resistance, we know that our final velocity is equal but in the opposite direction as the initial velocity. Therefore, we get:
At this point, the ball is at it's original height of , but traveling downward at a rate of .
We can then use the following expression to calculate the velocity of the ball as it hits the ground:
Plugging in our values:
Then using our original expression again:
Adding our times together:
Example Question #81 : Motion In One Dimension
A plane is getting ready to take off and starts down the runway. The plane accelerates down the runway at a rate of and after seconds, it lifts off. How long did it travel on the runway before taking off?
For this problem, the following kinematic equation is necessary:
Since the plane starts at rest, we can simplify the equation to
The problem defines the acceleration to be and the time to be seconds so
Example Question #81 : Motion In One Dimension
A feather is dropped on the moon from a height of meters. How long does it take for the feather to fall to the surface?
For this problem, the following kinematic equation is necessary:
Since the feather starts at rest, we can simplify the equation to
The problem defines the acceleration to be . Since the acceleration is in the downward direction (towards the surface), it is more appropriately written as . The distance is meters (also in the downward direction). Therefore,
Example Question #83 : Motion In One Dimension
An ant travels along a taut string of length feet in minutes. What is the ant's average velocity in meters per second?
First we convert our units to SI, feet is meters and minutes is seconds. Now we combine this dividing by to arrive at our average velocity of