AP Physics Chapter 2 Study Guide
Motion in One-Dimension
Identify the time or times (if any) at which the two balls have the same speed.
Do A and B ever have the same speed? If yes, at what time?
At which point(s) is the object moving the fastest?, at rest?, slowing down?
Draw the position versus time, and velocity versus time graph for the diagram above.
Describing Motion
First, some sign conventions:
For position
For velocity
Motion Diagrams and Graphs
Example: Position data for a student walking to school.
Lets construct a motion diagram.
Now we want to create a position versus time graph for the student's data.
Since, the student walks at constant speed for the three intervals we can draw lines for the three intervals.
Example
Describe the motion of the car.
Here is a motion diagram of a car moving along a straight stretch of read.
Which of the following velocity versus time graphs matches the above motion diagram?
How do you calculate velocity from a position versus time graph?
Example:
A graph of position versus time for a lacrosse midfielder moving down the field appears as follows:
Which of the following velocity graphs matches the above position graph?
Uniform Motion
First Kinematic Equation
Solve this equation for 
.
Example:
A soccer player is 15 m from her opponent's goal. She kicks the ball hard; after 0.50 s, it flies past a defender who stands 5 m away, and continues toward the goal. How much time does the goalie have to block the kick from the moment the ball leaves the kicker's foot?
Example:
Cleveland and Chicago are 340 miles apart by train. Train A leaves Cleveland going west to Chicago at 1:00 p.m., traveling at 60 mph. Train B leaves Chicago going east to Cleveland at 2:00 p.m., going 45 mph. At what time do the two trains meet? How far are they from Chicago at this time?
From Position to Velocity
Looking at the student walking to school again.
Calculate the velocity during each section of the walk.
Create a velocity versus time graph from this data.
From Velocity to Position
Example:
A trolley travels along a straight run of track and the figure is a plot of its velocity versus time. Approximately how far did it travel in the first 3.0 s of its journey? How far from its starting point is it at t = 6.0 s? Draw a possible position versus time graph.
Motion with Changing Velocity
Instantaneous Velocity - is the velocity at which an object is moving at any given instance.
Finding the instantaneous velocity:
Acceleration
Acceleration is the rate at which an object's velocity changes with time.
Acceleration is the slope of the velocity versus time graph.
Example:
Signs of Acceleration
Kinematic Equations for Constant Acceleration
Example:
A car starts with an initial velocity of 5 m/s and an acceleration
of 
.
Determine:
(a) How fast is the car moving after it has traveled 100 m.
(b) How long does the car take to cover the distance of 100 m?
Example:
A particle starts with initial speed 
from
the origin (0, 0) and moves in the positive x direction with an acceleration
of 
.
Determine:
(a) Time t when the particle stops momentarily.
(b) The distance x when the particle stops momentarily.
(c) Time when the particle returns to the origin (0, 0).
(d) The speed of the particle at x = 100 m.
(e) The time t when x = 100 m.
(f) The time t when x = -100 m.
(g) On the coordinate systems below, draw the graphs for t = 0 to t = 30
seconds.
Example:
Chameleons catch insects with their tongues, which they can
extend to great lengths at great speeds. A chameleon is aiming for an insect
at a distance of 18 cm. The insect will sense the attack and move away
50 ms after it begins. In the first 50 ms, the chameleon's tongue accelerates
at 
for
20 ms, then travels at constant speed for the remaining 30 ms. Does its
tongue reach the 18 cm extension needed to catch the insect during this
time?
Example:
Cheetahs can run at incredible speeds, but they can't keep
up these speeds for long. Suppose a cheetah has spotted a gazelle. In five
long strides, the cheetah has reached its top speed of 27 m/s. At this
instant, the gazelle, at a distance of 140 m from the running cheetah,
notices the danger and heads directly away. The gazelle accelerates at 
for
3.0 s, then continues running at a constant speed that is much less than
the cheetah's speed. But the cheetah can only keep running for 15 s before
it must break off the chase. Does the cheetah have dinner or does it go
hungery?
Free Fall
When you drop an object, a ball for example, it will undergo a constant acceleration towards the earth.
A motion diagram for free fall would look like the diagram below:
Example:
A salmon is dropped by a hovering eagle. How far will the fish fall in 2.5 s? Ignore air resistance.
Example:
A ball is thrown straight down from the roof of a dormitory at 10.0 m/s. If the building is 100 m tall, at what speed will the ball hit the ground? How long will the trip take?
Example:
A .32 caliber bullet fired from a revolver with a 3 in long barrel will have a relatively low muzzle speed of about 200 m/s. If it's shot straight up, neglecting air resistance, (a) what is the peak height the bullet will reach? (b) How fast will it be moving when it returns to the height of the gun? (c) How long will the whole trip take?
Example:
A ball is hurled straight up at a speed of 15.0 m/s, leaving the hand of the thrower 2.00 m above ground. Compute the times and the ball's speeds when it passes an observer sitting at a window in line with the throw 10.0 m above the point of release.
Example:
Spud Webb, height 5 ft 7 inches, was one of the shortest basketball players in the NBA. But he had an impressive vertical leap: He was reputedly able to jump 110 cm off the ground. To jump this high, with what speed would he leave the ground?
Example:
A football is punted striaght up into the air; it hits the ground 5.2 s later. What was the greatest height reached by the ball? With what speed did it leave the kicker's foot?
Example:
Passengers on the The Giant Drop, a free fall ride at Six Flags Great America, sit in cars that are raised to the top of a tower. The cars are then released for 2.6 s of free fall. How fast are the passengers moving at the end of this speeding up phase of the ride? If the cars in which they ride then come to rest in a time of 1.0 s, what is the acceleration (magnitude and direction) of this slowing down phase of the ride? Given these numbers, what is the minimum possible height of the tower?
Example:
When you stop a car on icy pavement, the acceleration of
your car is approximately 
.
If you are driving on icy pavement at 30 m/s (about 65 mph) and you hit
the brakes, how much distance will your car travel before coming to rest?
Example:
As we will see in a future chapter, the time for a car to come to rest in a collision is always about 0.1 s. Ideally, the front of the car will crumple as this happens, with the passenger compartment staying intact. If a car is moving at 15 m/s and hits a fixed obstacle, coming to rest in 0.10 s, what is the acceleration? How much does the front of the car crumple during the collision?