ch2_dgesrk


 * Chapter 2 — Motion in One Dimension **



Section 2.1 — Displacement and Velocity
Displacement is a magnitude and direction.
 * __Displacement__**- The straight line drawn from the object's initial position to the object's new position.

math \Delta x=x_f-x_i math

**Reminder:** The displacement distance is not always equal to the distance traveled.

For instance, if you ran one lap around the track your displacement would be 0 meters not 400 meters because you started and ended at the same place.

The distance traveled in an interval is the area under the graph of a v vs t graph.

Remember to always set up a useful frame of reference. For instance, if all your measurements are downward that call downward the positive direction. However if you do this, be sure to specify the direction down in your answer.
 * __Frame of Reference__**- The point you have chosen to take your measurement's from.

Velocity is both a magnitude and direction. Speed is the absolute value of the magnitude of the velocity. The velocity of an object can also be found by finding the area under the graph of an a vs t graph.
 * __Average Velocity__**- The displacement in a certain amount of time.

math v_a_v_g=\frac{\Delta x}{\Delta t}=\frac{x_f-x_i}{t_f-t_i} math


 * __Instantaneous Velocity__**- The slope of the line tangent to the graph of //x// vs. //t// at the point of interest.


 * Useful equation for displacment: **

math \Delta x=\frac{1}{2}(v_i+v_f)\Delta t math

**1. Every morning you drive to good old Mt. Lebanon High School. Your house is a .53 hour trip from the school when you drive to school with an average velocity of 19 km/hr to the west. What is the displacement you have traveled to get to the school? 2. You decide that you would like to do nothing better on your Saturday afternoon than to calculate the average velocity of a turtle walking in a straight line. So you time the turtle and it takes him 5.0 minutes to move 2.0 meters left what is the average velocity of the turtle? 3. Mr. Strong decides that he wanted to run a marathon. He ran 12 yes, 12 kilometers east in a blazing time of 1 hour and 30 minutes what is his average velocity for the marathon?
 * How about some review problems

**1. 10.1 kilometers west is the displacement. 2. The average velocity is 6.7 x 10^-3 left. 3. Mr. Strong's average velocity is 8.0 kilometers per hour east.
 * Answers

Remember that acceleration like displacement and velocity also has a magnitude and direction.
 * __Average Acceleration__**- The rate of change in the object's velocity.

math a_a_v_g=\frac{\Delta v}{\Delta t}=\frac{v_f-v_i}{t_f-t_i} math


 * __Instantaneous Acceleration__-** The slope of the line tangent to the given point on the //v// vs. //t// graph.

Acceleration does not always have the same sign as the objects velocity. The sign of the acceleration just lets you know if they velocity of the object is increasing or decreasing.

**Useful equations involving acceleration:**

math v_f=v_i+a\Delta t math

math \Delta x=v_i\Delta t+\frac{1}{2}a\Delta t^2 math

math v_f^2=v_i^2+2a\Delta x math

 **Review Problems** 1. What is the acceleration of a dog that runs at a constant speed of 5 m/s right. 2. A man on a bike is riding in a straight line with a velocity of 5 m/s left and he accelerates at 0.75m/s^2 left, this boosts the bikers velocity to 8 m/s left. What is the time period that it took the biker to accelerate up to 8 m/s? 3. A car that has an initial velocity of 20 m/s right accelerates by 1 m/s^2 right for 7 seconds. What is the final velocity of the car?
 * Note **: These equations only work if the acceleration is constant. However, I can not think of a problem we have dealt with in class that does not have a constant acceleration.

**Answers** 1. The acceleration is 0 m/s^2 right because the dog is running at a constant speed 2. It takes 4.0 seconds. 3. The final velocity is 27 m/s.

**Section 2.3 — Falling Objects**

The free fall acceleration of all objects are the same. The mass does not matter.
 * __Free fall__**- The constant acceleration all objects fall at near the surface of the Earth without air resistance.

On the Earth the free fall acceleration is 9.81 m/s^2 and it is directed towards the Earth's surface, so it is actually is -9.81 m/s^2.

=Helpful Hints=

Every question of one dimensional motion will give you all of the variables, but one and you will be asked to solve for that one. If for some reason you don't have enough variables to plug into an equation you can manipulate the other equations, so that you can solve for one variable and then the other.

Additional info:

The graph of a position function is a parabola. The graph of a velocity function is a line with a slope other than 0 unless the acceleration is 0. The graph of an acceleration function is a horizontal line. Therefore the acceleration is always constant because no matter what the x value the y value will be the same.