MCAT Physical : Newtonian Mechanics and Motion
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Example Questions
Example Question #21 : General Principles
A runner completes a lap on a circular track in three minutes. The track has a radius of 210ft. The runner ran at a constant speed around the track.
What was the runner's average speed around the track?
Since 
Now, we can solve for speed using our equation. With 60 seconds per minute, 3 minutes is equal to 180 seconds.
Keep in mind that the question asked for the average speed, not velocity. Had it asked for the average velocity, 
Example Question #14 : Displacement, Velocity, And Acceleration
A velocity vs. time graph that shows the plotted line oscillating in a sinusoidal fashion. Which of the following scenarios could be represented by the sinusoidal line on the graph?
A man drives straight to work, only to find he forgot his briefcase. He quickly turns around and heads back home. He grabs it, and returns to work
A ball is thrown straight into the air and falls back to the ground
A runner does four laps around a circular track at a constant speed
A car drives in heavy traffic on a straight road, which causes it to accelerate and decelerate periodically
A projectile is launched at an angle from a tall cliff. Once it hits the ground, it bounces several times
A runner does four laps around a circular track at a constant speed
Keep in mind that velocity is a vector, and a change in direction results in a change in velocity. When a runner runs in a circular manner around a track, the velocity of the runner will oscillate between a maximum positive velocity and a minimum negative velocity. As a result, this scenario matches the velocity vs. time graph appropriately.
Example Question #15 : Displacement, Velocity, And Acceleration
A child throws a ball straight up into the air. He throws the ball with an initial velocity of 
The child catches the ball in his glove after it falls. What is the total displacement of the ball?
To solve this question, you must understand the difference between total distance and total displacement. While it is true that the baseball traveled a specific distance, the displacement is the final position of the baseball relative to the original position of the ball. The ball started and ended in the same place, so its total displacement is 0m.
Example Question #184 : Newtonian Mechanics And Motion
A child throws a ball straight up into the air. He throws the ball with an initial velocity of 
What is the vertical acceleration of the ball when it is at its peak height?
At its peak height, the ball will have a velocity of 
Example Question #361 : Mcat Physical Sciences
A ball is thrown straight up into the air. When the ball is at the top of its flight, what is its acceleration?
It depends on the initial velocity of the ball
Near the earth's surface (neglecting air resistance), all objects in free-fall accelerate downwards at 
Example Question #1 : Friction And Normal Force
A 
In this situation, we must simply remember how to calculate friction. Once the force of gravity overcomes the force of static friction, the object will slide. Our formula for friction is:
This means the force of friction is equal to the friction coefficient times the normal force. On an incline, the normal force is equal to the force of gravity times the cosine of the angle:
We can combine our formulas to give the force of friction.
Using the given coefficient of friction, mass, and angle, we can calculate the force of friction.
Example Question #1 : Forces
When the force applied to a moving object is equal and opposite the force of kinetic friction, what happens to the object?
It decelerates
It moves with a constant velocity
It accelerates
It stops
It changes direction
It moves with a constant velocity
It is important to understand the difference between static and kinetic friction. When an object is at rest, it takes more force to get it to start moving than to keep it moving. If you match the amount of static friction that can be generated when the object is at rest, it will not move because there is zero net force; the force applied must be greater than the static friction in order to initiate motion. Once the object begins moving, the force required to keep it moving decreases. If you match the force of kinetic friction, the object moves at a constant velocity because there is again no net force. Any more force will cause acceleration, while any less will cause deceleration.
Example Question #3 : Friction And Normal Force
A 
The block will suddenly jerk to the right, and then stop
The block will move to the right at a uniform velocity
The block will move to the right proportional to the force applied to it
When the block begins to move, it will smoothly accelerate to the right
The block will not move until the spring scale reads
The block will suddenly jerk to the right, and then stop
This is a classic experiment to determine the coefficient of static friction, 
When the frictional force is just barely overcome, the block will start moving to the right, but as soon as it does, the tension in the spring diminishes and static frictional forces prevail. The block thus starts moving and almost immediately stops.
Example Question #4 : Friction And Normal Force
A 
In this question, the net force on the block is zero. We know from Newton's second law that any non-zero force will produce an acceleration, resulting in movement of some sort. Since the block is at rest, and not moving, we can conclude that the net force is zero.
The forces acting on the block are the force of gravity, pulling the block downward, and the normal force, pushing the block upward. The force of the block on the table will be the force from gravity, while the force of the table on the block will be the normal force. Since these are the only two forces acting on the block, we can add them together to get the net force.
Reorganizing the equation, we can set the two forces equal. This is a reflection of Newton's third law.
Gravitational force is equal to the mass of the object times the acceleration from gravity.
Using these values, given in the question, we can find the normal force, or the force of the table on the block.
The final normal force is positive because it acts in the upward direction, opposite of gravity.
Example Question #2 : Forces
Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top.
They then decide to sled down the hill, but disagree about who will go first.
Scenario 1:
Sam goes down the hill first, claiming that he will reach a higher velocity. If Sally had gone first, Sam says they could collide.
Scenario 2:
Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.
Scenario 3:
Unable to agree, Sam and Sally tether themselves with a rope and go down together.
Who would you expect to experience a greater force of friction while traveling down the hill?
Sam, because he experiences a greater normal force
Sam, because he travels more quickly
Sally, because she travels more slowly
Sally, because she experiences less normal force
They would experience equal forces of friction because the coeffecients of friction are the same for both.
Sam, because he experiences a greater normal force
The force of friction can be found from the following equation.
Force of Friction = Normal Force * Coeffecient of Friction
Normal force here is the force that the Earth pushes back on Sam against his mass. Thus, because he is more massive, he will experience a greater normal force and greater frictional force as a result.
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