Chapter 13 contains Review Questions Answers and Explanations.
The components are doubled.
The direction is 130o.
Consider an airplane taking off at an angle of 10o.
The airplane has traveled a total of 140 m through the air.
There are quantities that have both direction and magnitude.
The forces and velocities are important physical quantities.
The arrow can be used to represent the Vectors numerically with components or with a magnitude and direction.
If you draw the first and then start the second at the end of the first, you can subtract the first and then start the second at the end of the first.
Adding or subtracting individual components can be used to add or subtract Vectors.
If the scalar is negative, multiplying a vector by it can change the length or direction of it.
Chapter 4 Kinematics is moving.
The father of modern physics stated a distinction between the cause of motion and description of motion.
The mathematical tools for describing motion are called keematics.
An object's location is determined by its position.
In mathematics, we use a coordinate system to show where an object is located since it is difficult to describe an object's location.
Positive and negative positions can be determined using a coordinate system.
We usually set the object in question as the origin and relate its surroundings to it.
It's the point at which the object's initial position is taken into account.
The distance from an object's final position and initial position is the displacement.
The total path taken is taken into account when calculating the net distance.
Different answers for a problem can be given by asking for displacement and total distance.
A rock is thrown upward from the edge of a 30 m cliff, then falling all the way down to the base of the cliff.
The object's initial position and final position are what Displacement refers to.
The rock started on the edge of the cliff and ended up on the ground 30 m below.
Its distance is 50 m, 10 m on the way up and 40 m on the way down.
If you want to do well on this test, you need to be proficient in basic trigonometry.
Find the runner's displacement for the race.
The runner's displacement is zero if she returns to where she left off.
You should be able to handle the questions graphically.
The position-versus-time graph is a popular graph.
The slope and basic area of geometric shapes are what you will have to brush up on.
It stopped at 1 s to 3 s and stayed 10 m away from where it started.
The initial position is subtracted from the final position.
That's -5 - 0 - -5 m, or 5 meters to the left, or negative direction.
The speedometer tells us how fast we're going, and it gives us our speed.
We're covering a distance of 10 meters every second.
The car's speed doesn't matter to the driver.
You could be driving north, south, east, or west.
The direction does not affect the speed.
We learned about displacement, which takes both distance and direction into account.
There is a distinction between speed and velocity.
There is speed plusdirection.
The speed is the magnitude of the velocity.
The average speed is not the magnitude of the average velocity.
The runner finishes the race in 1 minute and 18 seconds.
Average speed is the total distance divided by time.
The runner's average speed was 6.4 m/s since the track is 500 m. 0 m/s is the number.
If you set your car's cruise control at 55 miles per hour but turn the steering wheel to follow a curved section of road, then the direction of your velocity is not constant, even though your speed doesn't change.
If the velocity is constant, then both speed and direction are constant.
If speed were to change, the magnitude of the velocities would change.
The car's speed increases when you step on the gas pedal and decreases when you step on the brake.
The car's direction of motion can be changed by turning the wheel.
The rate-of change of an object's velocity is the same as the rate-of change of an object's position.
If the object's speed doesn't change, it can accelerate.
A change in magnitude or direction is known as acceleration.
A car is traveling in a straight line on the highway at a constant speed of 80 miles per hour for 10 seconds.
Find its speed.
The car is traveling at a constant rate of speed.
If there's no change in speed, there's no acceleration.
A car is travelling along a straight highway at a speed of 20 m/s.
3 seconds after the driver steps on the gas pedal, the car's speed is 32 m/s.
Find its average speed.
4 m/s2 is 12 m/s.
The driver of the car in example 8 slowed down from 32 m/s to 20 m/s in 2 seconds.
-2 m/s2 is equal to -12 m/s.
The direction of the acceleration is opposite of the direction of the velocity, which is what the negative sign means.
Its speed increased to 10 m/s over the first two seconds.
The velocity was steady at -5 m/s.
The object accelerated.
The slope of the graph gives theacceleration.
The object experienced a negative acceleration.
The object's speed was slowed until it reached 0 m/s.
The object began increasing its speed in the opposite direction.
The slope of the graph is zero.
The object experienced zero acceleration because the slope of the graph is zero.
The object did not move since it was in the negative direction.
5 m/s is 2 s.
The area between the graph and the horizontal axis has been determined.
There are positives and negatives to the concept.
The area can be negative or positive.
The object's displacement is equal to the axis.
15 m is 3 s/ 10 m.
The Big Five #1 equation is derived from this.
The relationship between speed and time is shown in a graph.
If an object's original direction of motion is positive, then an increase in speed corresponds to positive acceleration.
This is indicative of segments one and three.
In the top part of the segment, there is an indication of a decrease in velocity.
If an object's original direction is negative, an increase in speed corresponds to negative acceleration.
You are speeding up backward.
The object slows down when the velocity and acceleration are in opposite directions.
In the real world, there are many factors that affect uniform acceleration.
Everything is treated in ideal situations for the purposes of the AP physics 1 exam.
One restriction that will make our analysis easier is to only consider motion that takes place along a straight line.
There are only two possible directions of motion in these cases.
One is positive and the other is negative.
Most of the quantities we've been dealing with--displacement, velocity, and acceleration--are vectors, which means that they include both a magnitude and a direction.
The direction can be specified by attaching a sign to the magnitude of the quantity.
The fact that the quantities include direction will still be indicated by a positive or negative sign even if we abandon the use of bold letters.
We've seen quantities so far.
The equations are easier to write down with this simplification.
They work in cases where the speed is uniform.
Writing down what you are doing can help determine which Big Five equation to use.
The definition of Big Five #1 is the area under a velocity versus time graph.
The slope at any given moment of a velocity versus time graph is called Big Five #2.
The important three equations that can be used to solve a problem are Equations #1, #2, and #5.
To speed up problem-solving, it is advisable to memorize all five equations.
Its speed is 14 m/s.
If you remember to include the units in your final answer, it's okay to leave off the units in the middle of the calculation.
Leavingunits off your final answer will cost you points.
A car that is initially traveling at 10 m/s is able to accelerate uniformly for 4 seconds at a rate of 2 m/s2 in a straight line.
A rock is dropped off a cliff.
Initial velocity is not given in numerical terms by some problems.
We can assume our initial velocity is zero if we see the statement "starting from rest" or "dropped".
This makes sense, since the object moves downward and the gravity causes it to point downward.
Some graphs don't have nice straight lines.
Straight line segments are either constant slopes or constant velocities, depending on the type of graph.
Let's look at a question that might be asked about the curve.
This is familiar territory.
The instantaneous velocity is the speed at which things happen.
You can see the magnitude of your instantaneous velocity when you drive in a car.
A line that only touches a curved line.
We will need to approximate to find the instantaneous velocity.
The speed from 9 to 10 seconds is close to the speed at 10 seconds, but it is still slow.
The speed from 9-11 seconds is close to the speed at 10 seconds, but it is still too fast.
You can find the middle ground between the two ideas by looking at the slope of the line after 10 seconds.
This is very close to the instantaneous speed.
The line is close enough for our purposes, but it only touches the curve at one point.
Draw a line.
Pick any two points on the line to find the slope of the tangent.
When you start to understand that position-versus-time and velocity-versus-time graphs have a few basic shapes, you will be in a better position to see all the graphs.
Having a feel for the building blocks will help you understand the graphs in physics.
The following two graphs show something that isn't moving.
An object moving in the positive direction is represented by either of the two graphs.
An object moving in the negative direction is represented by either of the two graphs.
An object speeding up in the positive direction is represented by either of the two graphs.
There are two graphs that show an object slowing down in the positive direction.
Take the time to Familiarize yourself with the graphs so that you can quickly see what's happening in the graph.
An object slowing down in the negative direction is represented by either of the two graphs.
An object speeding up in the negative direction is represented by either of the two graphs.
There is a position-versus-time graph.
Part A is a constant speed moving away from the origin, part B is at rest, part C is speeding up moving away from the origin, part D is slowing down still moving away from the origin, and part E is speeding up moving back toward the origin.
It's a sign of a positive acceleration.
A negative acceleration is represented by curving down.
The average velocity is given by the area under the graph.
The greater the slope at a point of a graph, the faster it is.
The greater the slope at a point, the greater the speed.
The slope of the graph is called the acceleration.
The concept of slope still applies even though this graph is not composed of straight lines.
The slope is negative at points A and D and positive at points B and E.
The simplest real-life example of motion under constant acceleration is the motion of objects near the surface of the Earth and ignoring air resistance.
It can fall due to gravity.
A rock is dropped from a cliff.
Sometimes we don't have to set gravity as negative.
As long as you match the positive or negative with gravity, you can choose any coordinate system you want.
There is a negative in front of the 80 because the rock fell down.
A baseball is thrown with an initial speed of 20 m/s.
The Big Five equation is used.
The time it takes for an object to be thrown straight up is the same as the time it takes for an object to fall down.
An object is falling with a speed of 20 m/s after being thrown straight down.
The object in front of the 40 is moving in the down direction.
A baseball hit by a bat, a golf ball struck by a club, and a tennis ball hit from the baseline are examples of objects that don't follow a straight-line path.
The object will travel along a parabolic trajectory if we launch it at an angle other than straight upward and only consider the effect of gravity.
The horizontal and vertical motions are analyzed separately using the Big Five.
The key to projectile motion problems is this.
The magnitudes of each other are only affected by their directions.
It makes with the horizontal.
An object is thrown with a speed of 10 m/s.
4 seconds later, it hits the ground.
In standard motion, horizontal velocity is constant.
A ball with an initial speed of 15 m/s is thrown from a height of 100 m.
The ball doesn't strike the ground before the two seconds have elapsed because the initial vertical position is 100 m above the ground.
A projectile is traveling in a path for 6 seconds.
There is no horizontal acceleration because of gravity, which is purely vertical.
If there is no horizontal acceleration, the projectile's horizontal velocity 1 s after it's launched is the same as its horizontal velocity 3 s later.
An object is projected upward with a launch angle of 30 degrees and an initial speed of 40 m/s.
For the vertical component of motion, you can refer to it as throwing an object straight up and it falling down.
The object is only part of its time of travel.
An object is projected upward with a launch angle from the ground and an initial speed of 60 m/s.
It should return to its original height.
Because the parabola is symmetrical, the total time the object spends in the air is equal to twice the time required to reach the top of the trajectory.