The slope of the curve (or slope of the tangent line to the curve) decreases in time.

1. A train car moves along a long straight track. The graph shows the position as a function of time for this train. The graph shows that the train: 1. speeds up all the time. 2. slows down all the time. 3. speeds up part of the time and slows down part of the time. 4. moves at a constant velocity. The slope of the curve (or slope of the tangent line to the curve) decreases in time.

2. The graph shows position as a function of time for two trains running on parallel tracks. Which is true? 1. At time tB, both trains have the same velocity. 2. Both trains speed up all the time. 3. Both trains have the same velocity at some time before tB. 4. Somewhere on the graph, both trains have the same acceleration. The slopes of the two curves (or the tangent lines to the curves) are parallel at some point prior to tB.

3. Freefall – a specific example of 1D motion What is freefall? Motion towards the Earth only due to gravitational attraction. Close to the surface of the Earth it is commonly discussed as vertical motion. Gravitational attraction causes an object to be accelerated towards the surface of the Earth. Near the surface of the Earth this acceleration is assumed to be constant. It is not actually constant it changes with altitude and latitude. • If we assume up is a positive direction the direction of g would be negative. • You can define down as a positive direction. • Make sure you specify your positive coordinate directions. • Once you choose your directions for a specific problem do not change them!!

4. A ball is thrown upward with an initial speed of 20 m/s. What is the velocity, and acceleration at point 0? What is its velocity and acceleration at point 1 after 1 s? What is its velocity and acceleration at point 2? What is its velocity and acceleration at point 3, 1 s after point 2? What is its velocity and acceleration at point 4? What is its velocity and acceleration at point 5, 3 s after point 2? v = 20 m/s and a = -9.8 m/s2 2 v = 10.2 m/s and a = -9.8 m/s2 3 1 v = 0 m/s and a = -9.8 m/s2 v = -9.8 m/s and a = -9.8 m/s2 4 0 v = -20 m/s and a = -9.8 m/s2 5 v = -29.4 m/s and a = -9.8 m/s2

5. If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s2. If instead you throw it downward, its downward acceleration after release is 1. less than 9.8 m/s2. 2. 9.8 m/s2. 3. more than 9.8 m/s2.

6. A person standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial speed. Neglecting air resistance, the ball to hit the ground below the cliff with the greater speed is the one initially thrown 1. upward. 2. downward. 3. neither—they both hit at the same speed.

7. You are throwing a ball straight up in the air. At the highest point, the ball’s 1. velocity and acceleration are zero. 2. velocity is nonzero but its acceleration is zero. 3. acceleration is nonzero, but its velocity is zero. 4. velocity and acceleration are both nonzero.

8. A cart on a roller-coaster rolls down the track shown below. As the cart rolls beyond the point shown, what happens to its speed and acceleration in the direction of motion? 1. Both decrease. 2. The speed decreases, but the acceleration increases. 3. Both remain constant. 4. The speed increases, but acceleration decreases. 5. Both increase. 6. Other

9. CH 3: Motion in 2D

10. Do more objects move in 1D or 2D? 2D – most object do not move in a completely straight line with no side to side motion or up and down motion. • Examples of 2D motion: • car going around a corner • moves forward and to the right at the same time • car traveling straight on a rough road • moves forward and up and down at the same time • thrown object • moves forward and up or down at the same time • merry – go – round • moves forward and to the right at the same time What do you notice that is similar about the examples listed above? All of them refer to “at the same time”. This is the means by which we link the two different motions together. 2D motion is really just two different 1D motions. These two distinct motions are often not related. The mathematical models we use to describe 2D motion are the same ones we used for 1D motion. The main difference would be notation.