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2.4 Acceleration

- If you've spent a lot of time driving, you probably have a good idea of how fast you're going.

- 40 miles is the distance between the two stations.

- A plane slows down as it comes in for a landing.
- Its speed is opposite of its direction.

- To accelerate means to speed up.
- The car's acceleration can cause it to speed up.
- The formal definition of acceleration is more inclusive.

- The SI units for acceleration are meters per second squared or meters per second per second, which means how many meters per second the velocity changes every second.

- It has both magnitude and direction.
- A change in speed can be a change in magnitude, but it can also be a change in direction.
- If a car turns a corner at a constant speed, it will accelerate because its direction is changing.
- The quicker you turn, the faster you accelerate.
- There is an acceleration when velocity changes in either direction or magnitude.

- The change in velocity is the same as the acceleration.
- It can change in magnitude or direction.
- A change in speed or direction is Acceleration.

- Although acceleration is in the direction of the change in velocity, it is not always in motion.

- The direction of an object's motion affects its acceleration.

- A subway train coming into a station.
- It is moving in a different direction.
- Deceleration is the opposite of the direction of the velocity.
- Speed is reduced by Deceleration.
- The chosen coordinate system has negative acceleration in it.

- Negative acceleration may or may not be considered negative.

- Figure 2.14 is an example.

- Positive acceleration is present in our coordinate system.
- It has negative acceleration in our coordinate system because it is toward the left.
- The direction of the car's acceleration is opposite to its direction of motion.
- It is positive because it is toward the right.
- The car is decelerating because of its acceleration.
- It is going to the left with negative acceleration.
- It is speeding up because it is in the same direction as its motion.

- We assign a coordinate system to the problem after drawing a sketch.
- It's a simple problem and it helps to visualize it.
- We assign the east and west to be negative.
- Negative velocity is what we have in this case.

- The knowns should be identified.

- The horse's final speed is equal to its change in velocity.

- Plug in the known values and solve for the unknown.

- The negative sign indicates that the acceleration is going to the west.
- The horse increases its speed by 8.33 m/s due west each second, which we write as 8.33 meters per second.
- The ride is not smooth and this is an average acceleration.
- The rider would have to hang on with a force equal to his weight because of the magnitude of the acceleration.

- The average over the entire interval is nearly the same as the instantaneous acceleration.
- The motion should be treated as if it had a constant acceleration equal to the average.
- It is a good idea to choose an average acceleration for each time interval.

- The average over the interval is the same as the acceleration.
- It is necessary to consider small time intervals with constant or nearly constant acceleration.

- The shuttle moves to the right and left.
- The examples are designed to show some of the reasoning that goes into solving problems.

- The - axis means to the right and the left for displacements, velocities, and accelerations.
- Its displacement is less than 2.0 km.

- A drawing with a coordinate system is already provided, so we don't need to make a sketch, but we should analyze it to make sure we understand what it is showing.
- The equation is used to find displacement.
- The initial and final positions are given.

- The knowns should be identified.
- We can see that for part a and part b in the figure.

- The displacement of the motion in (a) is to the right and thus has a positive sign, while the displacement of the motion in (b) is to the left and thus has a negative sign.

- Think about the definitions of distance and distance traveled and how they are related to displacement to answer this question.

- The total length of the path between the two positions is called distance traveled.

- The displacement was +2.00 km.
- There was a distance between the initial and final positions.

- The distance between the initial and final positions was 1.50 km.

- There is a distance.
- There is no sign of direction.

- There are three steps to this problem.
- First we have to determine the change in velocity, then we have to determine the change in time, and finally we have to use these values to calculate the acceleration.

- The knowns should be identified.

- Plug in known values and solve for the unknown.

- We have both hours and seconds for time, so we need to convert everything into SI units of meters and seconds.

- acceleration is to the right if the plus sign is used.
- The train starts from rest and ends up going to the right.
- The change in velocity is always the same as the change in acceleration.

- The train is decelerating because it is toward the left.
- In the previous example, we had to find the change in velocity and the change in time and solve for it.

- The knowns should be identified.

- Plug in the knowns and solve the problem.

- acceleration is to the left according to the minus sign.
- The sign is reasonable because the train initially has a positive speed, and a negative speed would oppose the motion.
- The change in velocity is negative and acceleration is in the same direction.
- This acceleration can be called a deceleration because it has a different direction.

- The train's position changes slowly at the beginning of the journey, then more and more quickly as it picks up speed.
- At the end of the journey, its position changes more slowly.
- The position changes at a constant rate in the middle of the journey.
- At the beginning of the journey, the train's speed increases.
- There is no change in the middle of the journey.

- The train decelerates at the end of the journey.
- At the beginning of the journey, the train has positive acceleration.
- In the middle of the journey, it doesn't have any acceleration.
- It slows down at the end of the journey.

- The average displacement is divided by time.
- Since the train moves to the left, it will be negative here.

- The knowns should be identified.

- The motion to the left is indicated by the negative velocity.

- We need to find the change in time and the change in velocity to calculate average acceleration.

- The knowns should be identified.

- acceleration is to the right if the plus sign is used.
- The train initially has a negative velocity to the left and a positive acceleration to the right, so this is reasonable.
- The change in velocity is positive because acceleration is in the same direction.

- The signs of the answers are the most important thing to note about these examples.
- The quantity is to the right and the minus is to the left.
- This is easy to imagine.

- It is not obvious for acceleration.
- Negative acceleration is seen as the slowing of an object by most people.
- The difference was that the acceleration was in the opposite direction.
- A negative velocity will be increased by a negative acceleration.
- Both are negative.
- The directions of the accelerations are given by the plus and minus signs.
- The object is speeding up if it has the same sign.
- The object is slowing down if it has the opposite sign.

- The airplane will have negative acceleration if we take east to be positive.
- Its speed is opposite in direction.

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