Presentation on theme: "If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s 2. If instead you throw it downward, its downward acceleration."— Presentation transcript:
If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s 2. If instead you throw it downward, its downward acceleration after release is 1. less than 9.8 m/s 2. 2. 9.8 m/s 2. 3. more than 9.8 m/s 2.
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.
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.
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
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 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. 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.
Position, Velocity and Acceleration in 2D Position in 2D Displacement in 2D Velocity in 2D Acceleration in 2D There are no changes to the definitions of these quantities, but we must remember that there are two components for each vector!!
2D Motion with Constant Acceleration The constant acceleration equations are derived in an identical fashion to the way they were derived in 1D. They will not be re-derived here, but rewritten to include 2D. Differentiating vectors or and The subscripts show the direction we are working with, so we can ignore the unit vectors while working with the equations in this form. or and The x and y directions are completely independent of each other!!
Example: A particle moves in a horizontal xy-plane. It’s x and y positions as a function of time are given below. Write an expression for the a) position, b) velocity and c) acceleration in vector form. a) b) c)